What is a "lemma"?

Question

As per title, what is a "lemma"? How is it different from "theorem"?

ASAIK, I have to prove a self-proposed theorem in my paper. Do I also have to provide the proof for a self-proposed lemma?

Answer 1

Short answer, they are the same, and yes, you need to prove it. From Wikipedia

There is no formal distinction between a lemma and a theorem, only one of intention – see Theorem terminology.