A player account is for somebody who wants to train with the Touch Trainer. A trainer account is for somebody who wants to train other players. When you first create an app account (see article), you will be asked if you are a trainer or a player.
However, if at some point that changes, you can always add trainer privileges by going to SETTINGS and checking the "Trainer Privileges" box. By doing so, every time you train you will get the option of being a trainer or player.
If you have enabled trainer privileges, you can tap the toggle switch between being a player and a trainer in the session. This is useful if you take on trainer and player roles in different situations.