[samatman]

But where is the line?

Proof A and Proof A' are identical, except that Proof A says "and therefore" where Proof A' says "and so we see that". Different proofs?

Proof A'' is a faithful translation of Proof A into French, is it now different? Or is it a trivial translation of the same proof into different language?

This is, in fact, the topic of the Fine Article. The layman (myself included) sees easily that proof is something more durable than the exact words chosen, or even the language the proof is written in. Mathematicians (and patzers such as yours truly) will tend to view trivial transformations of a step in a proof, or trivially equivalent tactics, as resulting in the same proof.

What makes such a transformation trivial? Good question.