A lot of the best Pokemon Trainer amiibo were trained at the start of the scene, when only the Charizard amiibo was available. As a result, these Trainers all have to start with Charizard and then switch to Squirtle afterwards. However, recently the Ivysaur, Squirtle and Pokemon Trainer amiibo were released, which allows us to experiment with how they’re affected when you transplant one into the other.
We know already that Pokemon Trainer, the character, functions as a three-way brain transplant. If you teach Squirtle to use neutral special, Ivysaur and Charizard do too. This is because they all share the same set of moveset probabilities between three unique characters. In a sense, each time the amiibo switches characters they’re transplanting Ivysaur into a Charizard FP.
As it turns out, if you transplant one Pokemon into another, or into Pokemon Trainer, almost nothing happens. They still play the same way and use the same moves. This is unique in all of Smash, because any other character that has a brain transplant, even Echo Fighters, will play a bit differently and be affected by it.
There are a few changes that are important to take note of. If you take your Charizard amiibo and transplant it into Squirtle or Ivysaur, the amiibo will function identically but the Pokemon they start with will be different. So you can use that to shift around who you want first. If you transplant that same Charizard into Pokemon Trainer, (who is unique in that you can choose which Pokemon to start with before the battle) the Pokemon Trainer will start with Charizard by default.
Basically, the only function of transplanting a Pokemon into another Pokemon is changing what character they start as.