Generally when people say something is a "myth", they mean it's not true:
"Are all bats blind?"
"No, that's just a myth."
There's nothing wrong that that, of course, but there's a richer, older, meaning of myth: A story we tell to explain something in the world. In that sense, a myth is a story of the form "This is the way it is because so-and-so did thus-and-such" (many constellations have stories like this associated with them) or "So-and-so did this so that thus-and-such" (the story of Prometheus bringing fire to humanity is a famous example).
The word theory is also used in two senses. Generally, people use it to mean something that might be true but isn't proven.
"I personally think that the Loch Ness monster is actually an unusually large catfish, but that's just a theory."
In science, though, a theory is a coherent explanation of some set of phenomena, which can be tested experimentally. There are a couple of related senses of theory, for example mathematical sense of theory, as in group theory, meaning a comprehensive framework that brings together a set of results and sets the direction for future research. While there's no element of experimental evidence, the goal is still to understand and explain.
For example, Newton's theory of universal gravitation explains a wide variety of phenomena, including apples falling from trees, the daily tides of the sea and the motion planets in their orbits, by positing that any two massive bodies exert an attractive force on each other, and that this force depends only on the masses of the bodies and the distance between their centers of gravity (more precisely, it's the product of the two masses, divided by the square of the distance, times a constant that's the same everywhere in the universe).
Newton's theory is actually incorrect, since it gives measurably incorrect results once you start measuring the right things carefully enough. For example, it gets Mercury's orbit wrong by a little bit, even after you account for the effects of the other planets (particularly Jupiter), and it doesn't explain gravitational lensing (an image will be distorted by the presence of mass between the observer and what is seen).
Newtonian gravity is still taught anyway, since effects like these don't matter in most cases and it's much easier to multiply masses and divide by distance squared than to deal with the tensor calculus that General Relativity requires.
My point here is that, as with myths, the ability to explain is more important than some notion of objective truth. As far as we currently understand it, Einstein's theory of gravity, General Relativity, is "true", while Newtonian gravity is "false", but Newton's version is still in wide use because it works just as well as an explanation, since in most cases it gives the same results for all intents and purposes.
Myths and theories both aim to explain, but there are a couple of key differences. First, myths are stories. Theories, even though they're sometimes referred to as stories, aren't stories in the usual sense. There is no protagonist, or antagonist, or any characters at all. Neither Newton's nor Einsteins theory of gravity starts out "Long ago, Gravity was looking at the sun in empty space, and thought 'I should make the planets go around it'" or anything like that.
Second, and perhaps more important, theories are not just explanations of things we already know, but the basis for predictions about things we don't know yet. In the famous photographic experiments of the eclipse of 1919, general relativity predicted that stars would appear in a different position in the photographs, due to the Sun's gravity distorting space, than the Newtonian version would predict (which was that they would be in the same place they'd be seen when the Sun wasn't between them and the Earth). There's some dispute as to whether the actual photographs could be measured precisely enough to demonstrate that, but there's no dispute that the effect is real, thanks to plenty of other examples.
Myths make no claim of prediction. If a particular myth says that a particular constellation is there because of some particular actions by some particular characters, it says nothing about what other constellations there might be. The story of Prometheus bringing fire to humanity doesn't predict steam engines or cell phones.
It's exactly this power of prediction that gives scientific theories their value. It's beside the point to say that some particular scientific theory is "just a theory". Either it gives testable predictions that are borne out by actual measurements, or it doesn't.
Science lives and dies by prediction--a fact which has kept noted climatologist Geo. F. Will strangely quiet lately.
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