Yes. Preflop, the big blind (or straddle) is the first bet. The open raise is the 2nd bet and a reraise would be a 3bet. Then 4bet etc.
The counter resets on every street so on the flop there are 0 bets until someone makes one. Then the first reraise is the 2bet but no one says that they just say they got check raised or reraised. Then if there is another raise it becomes a 3 bet and so on as long as there are more raises.