Skills in Persona 5 come in 6 categories: Physical, Magic, Recovery, Support, Ailment, and Passive. There are over a hundred skills in the game (trust me, I had to translate every single one of them) so you have a lot of room for customizing not only your own Personas, but those of your teammates as well.
All Personas have inclination towards certain types of skills. For example, a Persona from the Strength arcana is more likely to learn physical or passive skills. Take all of this into account when performing fusion!