Ahhh. There’s the rub. The classical answer to this question is if two organisms can mate and produce viable, fertile offspring, they’re in the same species. If not, they’re not. A better answer is if genes can flow between two populations by interbreeding, then they’re in the same species. This takes care of situations like that frog that’s spread along the east coast, where nearby populations can interbreed, but Florida frogs can’t breed with Virginia frogs. Genes can still spread all the way up and down, so they’re still one species.
But with some organisms, especially birds and insects, figuring out who can or does breed with who can be extremely difficult. There’s quite a bit of educated guesses and reshuffling as new data appears. DNA analysis has proven to be very helpful with this.