Cold Calling

[CardRG]

First, a clarification: I thought cold calling was defined thusly: When a player calls 2 bets when that same player has not already bet during that particular street.

UTG bets; MP raises. You, the button, 3 bets. You just cold called.

But, if I understand correctly, this next example is different:

UTG bets; MP raises. You, the button, 3 bets. You just cold called. UTG puts in 2 more bets. UTG simply called a Reraise, not cold called a raise. Am I wrong?