Lemma vs. Theorem I've been using Spivak's book for a while now and I'd like to know what is the formal difference between a Theorem and a Lemma in mathematics, since he uses the names in his book. I'd like to know a little about the ethymology but mainly about why we choose Lemma for some findings, and Theorem for others (not personally, but mathematically, i.e. why should one classify a finding as lemma and not as theorem). It seems that Lemmas are rather minor findings that serve as a keystone to proving a Theorem, by that is as far as I can go.
NOTE: This question doesn't address my concern, so please avoid citing it as a duplicate.

There is no mystery regarding the use of these terms: an author of a piece of mathematics will label auxiliary results that are accumulated in the service of proving a major result lemmas, and will label the major results as propositions or (for the most major results) theorems.  (Sometimes people will not use the intermediate term proposition; it depends on the author.)
Exactly how this is decided is a matter of authorial judgement.
There is a separate issue, which is the naming of certain well-known traditional results,
such as Zorn's lemma, Nakayama's lemma, Yoneda's lemma, Fatou's lemma, Gauss's lemma,
and so on.  Those names are passed down by tradition, and you don't get to change them, whatever your view is on the importance of the results.  As to how they originated, one would have to investigate the literature.  
