Q:

Definition: Theorem, Lemma, Proposition, Conjecture and Principle etc.

Definition: Theorem, Lemma, Proposition, Corollary, Postulate, Statement, Fact, Observation, Expression, Fact, Property, Conjecture and Principle

Most of the time a mathematical statement is classified with one the words listed above.
However, I can't seem to find definitions of them all online, so I will request your aid in describe/define them.
Also, when is a mathematical statement a theorem versus a lemma ? I've read that a theorem is important while a lemma is not so important and used to prove a theorem. However a theorem is sometimes used to prove some other theorem. This implies that some theorems are also lemmas ?
Is it subjective with respect to the author, which statements become a theorem, lemma, etc. ?

A:

I have taken this excerpt out from How to think like a Mathematician

I think it does a great job of describing what those words mean in a sentence. Later in the chapter, he goes onto describe how we have some conjectures which have been called "Theorems" even though they weren't proven. For example, Fermat's Last Theorem was referred to as a Theorem even though it hadn't been proven. If you haven't read the book then I highly recommend it if you are a undergraduate in your first two years of math.

