There is no stylebook in mathematics dictating which term to use in which situation, as I think the earlier comments reflect. Every proved statement (even a corollary) might be labelled "theorem", but no one wants to go that far. For me a "lemma" is a technical step in a proof of something bigger, isolated for convenience and possibly for later use. (Unless the "lemma" acquires a life of its own, graduating to "Lemma".) A "theorem" means to me a major result, perhaps the goal of an entire paper. The use of "proposition" is most subjective, but it gets tedious to read a paper containing numerous secondary results claiming to be theorems. Even "corollary" is somewhat subjective, since it might follow instantly from an earlier result or else require other inputs and/or some cleverness to derive. In German there is "Satz" but also "Theorem" to confuse translators.