Depend of the coach.

Defense - You can only upgrade de defensive stats of the player, your player can upgrade their skill faster than the general one. 
Attack -  You can only upgrade de Offensive stats of the player, your player can upgrade their skill faster than the general one. 

...

Better the star more fast the player have an upgrade.

There is other variables like Player potential + Training Ground Level + Player Age + Coach Star +....
 

https://kickoffboss.com/pt-BR/blog/16/training-your-players-how-it-works-in-kickoff-boss