JPaco54,
1. Yes there is a difference, if we're talking the lexicon of the rules of baseball. Set is one of the two legal pitching positions defined in the rules (the other being windup), while the stretch is a "preliminary movement" which is explicitly legal for the pitcher to do before bringing his hands together and coming to a complete stop when pitching from the set position.
Colloquially, the two terms are often used interchangeably by people who have not actually read a rule book or when the discussion is not a technical "rules" discussion.
2. No, there is no definition of "preliminary movements" in the rule book, other than that they are something the pitcher does after engaging the rubber in the set position and prior to bringing his hands together. The stretch is specifically mentioned as an example of a legal "preliminary movement".
It is perfectly legal for a pitcher who has assumed the set position to make a (legal) pick-off throw to a base. He need not bring his hands together and stop before doing so. As a matter of fact, it is perfectly legal for him, in an attempt to deceive the runner, to begin his motion to come set and then
change to a pick-off as long as he does so in a continuous motion without interruption and steps legally to the base.
That always struck me as slightly odd in the context of the "...without alteration or interruption..." language. Nonetheless, it is so.
Finally, don't think, it can only hurt the team.
JM