Are all myths superstitions, or is it the other way around, i.e. all superstition being myths?
Or can these words basically be used interchangeably?
The dictionary definitions of these words seem somewhat vague.
Myth in its proper sense is a very rich and deep word, meaning a reflection of truth. Myths can be true, and they are intended to convey truth even when they are not, strictly speaking, true. Myth is a means of communicating non-empirical truth in an oral culture.
Superstition can have its roots in mythology, but is usually about actions performed without a proper understanding of the reasons.
Both words can have both negative and positive implications.
A myth is an echo of temporally distant events remolded into archetypes easily transmitted through oral histories. Myths are closely related to legends.
A superstition is “an unreasoning awe or fear of something unknown, mysterious, or imaginary, especially in connexion with religion.” [OED]
The two words need not intersect.
These two words are not interchangeable.
A myth is "any invented story, idea, or concept"
A superstition is "a belief or notion, not based on reason or knowledge, in or of the ominous significance of a particular thing, circumstance, occurrence, proceeding, or the like."
So the two words are definitely not interchangeable.
"Elephants are scared of mice" is a myth.
"Walking under a ladder brings bad luck" is a superstition.
A superstition is usually a belief that some event will bring either bad or good luck. In the broadest possible sense, a superstition could be considered a type of myth, but not vice versa.
Two definitions of myths per Merriam-Webster are:
1a : a usually traditional story of ostensibly historical events that serves to unfold part of the world view of a people or explain a practice, belief, or natural phenomenon
b : parable, allegory
2a : a popular belief or tradition that has grown up around something or someone; especially : one embodying the ideals and institutions of a society or segment of society
b : an unfounded or false notion
Myths refer to archetypal themes. Sometimes they are revered and sometimes they are debunked. Often they are so fanciful that their reality is highly unlikely (at least to the scientifically oriented). Sometimes they are unverifiable merely because they relate to things for which, thought feasible, there is no satisfactory scientific or historical record.
When a myth as described in the second definition is debunked and that debunking is widely disseminated, the myth dies.
Superstitions are beliefs that are not scientifically supportable (at least by current science). They are often tied to some religious belief, but sometimes just to random custom, e.g. step on a crack, break your mother's back.
If a reliable and valid proof of a superstition is later demonstrated, it ceases to be superstition and becomes emerging science. Probably the theory of germs was originally considered to be a superstition. (Mere speculation on my part.)
Most often superstitions are prescriptive or prohibitory. Do something/avoid something or suffer the consequences.
"Superstition" is generally defined as -- to take thefreedictionary.com as a source here -- "An irrational belief that an object, action, or circumstance not logically related to a course of events influences its outcome." A superstition is a claim of some supposed fact or relationship, like "if you break a mirror you'll get seven years bad luck" or "if a robin flies in your window, death will follow".
The word "myth" has multiple definitions.
Definition 1 in most dictionaries is that it is a "story" about gods or heroes. (We could discuss what makes some stories "myths" and other stories just ... "stories". But I don't think we need to get into that here.)
So a superstition is very different from definition #1 of a myth, because a superstition is not a story, it's just a statement. "If you break a mirror" etc is not a story: it has no plot, no characters beyond a generic "you", etc.
"Myth" often has a definition 2 that says something like, "a popular belief" or "a ficticious fact". Like someone may say, "It is a myth that blonde women are dumb," meaning that that statement is not true. This definition of myth could overlap with superstition, but they don't really mean the same thing. A superstition is generally understood to involve luck or magic; this definition of myth simply means "false claim", and is usually applied to things that have nothing to do with the supernatural. Callling something a myth is often a way to say it's not true without blatantly calling the person who said it a liar. Like if you say, "President Smith's claim that it was his jobs bill was what caused the stock market to go up is a myth", you are saying that the president's claim is not true, without explicitly saying that he is lying or stupid.
I see a couple of posters here have connected superstition with religion. I guess it depends on exactly how you define both words. I don't want to get into an argument about it, but I think such a connection is most often made by people who are denigrating someone else's religion or by atheists who are denigrating all religions. I have never heard anyone who was a serious believer of any religion refer to his own beliefs as "superstition". So I'd be cautious about using the word that way, unless it is your intent to insult someone's religion.
When we talk about superstition we are normally talking about things that are supposed to bring bad luck or good luck or cause some event that has no apparent causal relationship in any non-magical sense. I don't know of any religion that takes it as a point of doctrine that breaking a mirror will bring bad luck, for example. Calling something a superstition is normally understood to mean that it is irrational. If you say, "It is a doctrine of Christianity that Jesus Christ came back from the dead," that is a simple statement of fact. Of course many people doubt that that doctrine is true, but it is an undisputed fact that that is indeed a doctrine of orthodox Christianity. But if you say, "It is a superstition of Christianity that Jesus Christ came back from the dead", any Christian I know would interpret that as an insult, as saying that this belief is irrational and foolish. Of course if your intent is to call a belief irrational in an insulting way, then that may be an appropriate choice of words. But if you are trying to have a friendly conversation, use another word.
The English word Myth may be used in a sense which is somewhat similar to the usage for Superstition. However Myth has many shades of meaning, and many contextual uses, which have completely different meanings.
Something is called a "myth" in the sense used by the show Mythbusters; This is very similar in meaning to a superstition, but both could simply be dropped and replaced with "lies" or "misinformation".
Something which is a "myth" in the literary, or cultural sense is not a lie, and there is no intent to deceive. Myth refers to the powerful sense of meaning that certain stories have, even though they are not verifiable as history, or even though they are very unlikely to be true because they have elements that are either inconsistent, or supernatural, or otherwise, not very credible as literal history. Myth is more than legend, even. It's some kind of collective social identity.
The two are related in their sense of assumed tenuous relationship with truth, but they would only intersect (as descriptions of things) in something like 'just-so' stories, for example where the leopard got his spots. The second sense of myth, magical explanation, is synonymous with superstition. So some kinds of myths are superstitions (and some are not), but it would be misleading to say that a superstition is a kind of myth.
Superstitions inevitably have to do with the supernatural, and are mostly the result of religious practice/belief.
Myths are supposed "facts" pertaining to the natural and are caused by popularity of the statement, and how many people believe it. Additionally, myths can be proved/disproved.
For example, it is a superstition that clinking your glass scares away the Devil. This can't be proved and pertains to the supernatural. It is a myth that the reason meteors start glowing is because of friction (see this).