What do the words 'theory' and 'fact' really mean in science ?

People outside of science think that  a theory is an ordinary 'guess' or like any other 'belief'.

Some anti-science and to be more specific some anti-evolution people say 'evolution is just a theory'!

Just a theory? It is much much more than a word theory. If  somebody says it is just a theory, it shows  his or her willful ignorance. "Willful ignorance", of course, meaning that the person knows that the facts prove them wrong but just keeps pushing their beliefs anyway as an act of ill-advised stubbornness even though outside observers can easily see that they've long since lost the argument.

In other words, give it a rest already, just because you can't handle the truth doesn't mean you have to spend your life crusading to bring down the intelligence of others around you.

"Where is that good measure of self doubt which should drive scientists to keep digging and questioning every theory (even their own!) before it becomes entrenched?"

Self-doubt is a mandatory quality that every good scientist must have in spades. Certainty is the most critical attribute of religious, dogmatic, or ideological systems. Doubt is the most critical attribute of science. But once a fact has been established for the moment, it no longer is just a theory!

 In everyday use, theory means a guess or a hunch, something that still needs proof. In science, a theory is not a guess, not a hunch. It's a well-substantiated, well-supported, well-documented explanation for our observations and an explanation of some aspect of the natural world, based on a body of facts that have been repeatedly confirmed through observation and experiment. Such fact-supported theories are not "guesses" but reliable accounts of the real world. It ties together all the facts about something, providing an explanation that fits all the observations and can be used to make predictions. In science, theory is the ultimate goal, the explanation. It's as close to proven as anything in science can be.

The way that scientists use the word 'theory' is a little different than how it is commonly used in the lay public. Most people use the word 'theory' to mean an idea or hunch that someone has, but in science the word 'theory' refers to the way that we interpret facts of the moment.

Every scientific theory starts as a hypothesis. A hypothesis is an idea that hasn't been proven yet. If enough evidence accumulates to support a hypothesis, it moves to the next step — known as a theory — in the scientific method and becomes accepted as a valid explanation of a phenomenon.  A scientific theory is the framework for observations and facts. The scientific method is not guaranteed to give us the absolute truth. But it does give us our best understanding of it. And it gets closer to the truth over time. Bad theories get replaced with better ones. It is our only method of searching for actual truth. Theories may change, or the way that they are interpreted may change, but the facts observed in a given set of conditions themselves don’t change. But they can sometimes be modified when the set of conditions under which they are observed change. The form or shape of a theory might change as more and more facts are gathered. We have ample evidence of traits in populations becoming more or less common over time (evolution), so evolution is a fact but the overarching theories about evolution, the way that we think all of the facts go together might change as new observations of evolution are made. The fact is that Darwinian ideas are closer to truth than other 'theories' put forth before them. They explain everything we see in the past and present and quite often predict what we will find and where to find it. The details are debated endlessly, but the actual mechanism is as close to the truth as we can possibly hope for. The evolution theory was challenged several times but natural selection (in a slightly new form, with much stronger mathematical support and with a much more solid understanding of inheritance, for example) was returned to its place as the best theory that explained the observed facts of evolution.  In fact, natural selection can't explain everything about evolution.  That became clear when new data become available, especially when the molecular understanding of genetics became deeper in the 1960s.  The realization then was that while natural selection did seem explain a great deal about evolution, it wasn't enough to explain everything.  It wasn't necessary to completely reject the theory, but it was necessary to introduce added theories to explain different aspects of evolution. Therefore, the history of  theory of evolution by natural selection is one of constant attack, with scientists continually challenging it, extending it, finding its weaknesses and either replacing them with other theories or adding new evidence to strengthen it. 
A scientific theory is not the end result of the scientific method; theories can be proven or rejected, just like hypotheses. Theories can be improved or modified as more information is gathered so that the accuracy of the prediction becomes greater over time.

Theories are foundations for furthering scientific knowledge and for putting the information gathered to practical use. Scientists use theories to develop inventions or find a cure for a disease.

Some believe that theories become laws when they are proven, but theories and laws have separate and distinct roles in the scientific method. In science, we collect facts, or observations, we use laws to describe them, and a theory to explain them. You don't promote a theory to a law by proving it. A theory never becomes a law. In fact, if there was a hierarchy of science, theories would be higher than laws. There is nothing higher, or better, than a theory. A law is a description of an observed phenomenon that hold true every time it is tested. It doesn't explain why something is true; it just states that it is true. A theory, on the other hand, explains observations that are gathered during the scientific process. So, while law and theory are part of the scientific process, they are two very different aspects (1). .

The University of California, Berkley defines a theory as "a broad, natural explanation for a wide range of phenomena. Theories are concise, coherent, systematic, predictive, and broadly applicable, often integrating and generalizing many hypotheses." 

Any scientific theory must be based on a careful and rational examination of the facts. Facts and theories are two different things. In the scientific method, there is a clear distinction between facts, which can be observed and/or measured, and theories, which are scientists’ explanations and interpretations of the facts.

The Theory of Evolution by Natural Selection is our best explanation for the fact of evolution. It has been tested and scrutinised for over several years, and is supported by all the relevant observations. It isn't a theory; evolution is the observed fact that needs a theory to explain it.
If someone tries to tell you that evolution is just a theory, as a way of dismissing it, as if it's just something someone guessed at, remember that they're using the non-scientific meaning of the word.

And can there be actual facts in science? Does it make any sense for there to be? The answer is yes, but most of the claims which are assumed to be facts are not actually facts at all, at least not if you are speaking within the realm of scientific investigation.
A fact is a thing that is indisputable. It is a thing that is known to be true, especially when it can be proved. Or it is a truth known by actual experience or observation.
But in science, many facts are said to be "provisional truths." That means it is the truth for this moment! When new knowledge or data arrives and demands it, and when the conditions under which we observe them change, a fact can be modified!

This is what has happened when facts observed in the ordinary world showed different results in the quantum world! The facts are facts in the ordinary world only but they get modified when we switch to the other world!

Science is a process in which deductive reasoning is used to falsify models, using empirical evidence. All theories are just models which can be used to determine the nature of an outcome for a given experiment. We can say that an outcome occurs with probability 0 (is impossible), occurs with probability between (0, 1), i.e. is possible, or occurs with probability 1 (is necessary).

Truth in science is never final and what is accepted as a fact today may be modified or even discarded tomorrow. Scientific facts are generally believed independent of the observer: no matter who performs a scientific experiment, all observers agree on the outcome. There are also the social and institutional measures, such as peer review and accreditation, that are intended to promote factual accuracy (among other interests) in scientific study.

A scientific fact can therefore be summed up as an observation that has been confirmed repeatedly and is accepted as true but its truth is never final!

Like one scientist put it...Knowledge is like Schrödinger’s cat. Simultaneously reality and delusion. Truth and lie. The role of scientists is to slowly break into the box, listen to it, study it, so maybe, one day, we’ll find out whether our insights are dead or alive.

References:

1. http://web.missouri.edu/~hanuscind/8710/NSTA_Science101theorylaw.pdf