What's the difference between theorem, lemma and corollary?

Lemma is generally used to describe a "helper" fact that is used in the proof of a more significant result.

Significant results are frequently called theorems.

Short, easy results of theorems are called corollaries.

But the words aren't exactly that set in stone.

A lot of authors like to use lemma to mean "small theorem." Often a group of lemmas are used to prove a larger result, a "theorem."

A corollary is something that follows trivially from any one of a theorem, lemma, or other corollary.

However, when it boils down to it, all of these things are equivalent as they denote the truth of a statement.

Terence Tao (Analysis I, p. 25, n. 4):

From a logical point of view, there is no difference between a lemma, proposition, theorem, or corollary - they are all claims waiting to be proved. However, we use these terms to suggest different levels of importance and difficulty.

A lemma is an easily proved claim which is helpful for proving other propositions and theorems, but is usually not particularly interesting in its own right.

A proposition is a statement which is interesting in its own right, while

a theorem is a more important statement than a proposition which says something definitive on the subject, and often takes more effort to prove than a proposition or lemma.

A corollary is a quick consequence of a proposition or theorem that was proven recently.