How exactly does a lemma differ from another type of proposition (like a theorem or corollary)?

Question

How exactly does a lemma differ from another type of proposition (like a theorem or corollary)?

I think it is that lemmas are used to help prove theorems and coroallary are specific cases of theorems. Is this correct?

Answer 1

There is no formal difference between a "theorem" and "lemma".

As you have noticed, propositions tend to be called "lemmas" when the author's main purpose in proving them is as a stepping stone to proving something more interesting. But ultimately is is subjective what one considers "interesting" enough to be called a theorem.

There are also results that are important enough to have capitalized names and nevertheless are called lemmas, such as for example Zorn's lemma. This is sometimes a pure accident of history, but also sometimes to suggest that whereas the result does not look particularly interesting on its surface, it is a useful component for proving more substantial propositions.