TITLE: Lemma vs. Theorem
QUESTION [39 upvotes]: 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.

REPLY [5 votes]: I guess it will do no harm if I copy here relevant part from Wikipedia's Theorem#Terminology. I think it answers this question to some extent.
However, it is possible that some points here might be obsolete - the reference given for this at Wikipedia is Wentworth, G.; Smith, D.E. (1913). "Art. 46, 47". Plane Geometry. Ginn & Co. But I found the description given below fine.
This is taken from the current revision of the article.

A number of different terms for mathematical statements exist, these terms indicate the role statements play in a particular subject. The distinction between different terms is sometimes rather arbitrary and the usage of some terms has evolved over time. 

An axiom or postulate is a statement that is accepted without proof and regarded as fundamental to a subject. Historically these have been regarded as "self evident", but more recently they are considered assumptions that characterize the subject of study. In classical geometry, axioms are general statements while postulates are statements about geometrical objects. A definition is also accepted without proof since it simply gives the meaning of a word or phrase in terms of known concepts.
A proposition is a generic term for a theorem of no particular importance. This term sometimes connotes a statement with a simple proof, while the term theorem is usually reserved for the most important results or those with long or difficult proofs. In classical geometry, a proposition may be a construction that satisfies given requirements; for example, Proposition 1 in Book I of Euclid's elements is the construction of an equilateral triangle.
A lemma is a "helping theorem", a proposition with little applicability except that it forms part of the proof of a larger theorem. In some cases, as the relative importance of different theorems becomes more clear, what was once considered a lemma is now considered a theorem, though the word "lemma" remains in the name. Examples include Gauss's lemma and Zorn's lemma.
A corollary is a proposition that follows with little or no proof from one other theorem or definition.
A converse of a theorem is a statement formed by interchanging what is given in a theorem and what is to be proved. For example, the isosceles triangle theorem states that if two sides of a triangle are equal then two angles are equal. In the converse, the given (that two sides are equal) and what is to be proved (that two angles are equal) are swapped, so the converse is the statement that if two angles of a triangle are equal then two sides are equal. In this example, the converse can be proven as another theorem, but this is often not the case. For example, the converse to the theorem that two right angles are equal angles is the statement that two equal angles must be right angles, and this is clearly not always the case.