Why are there different types of trainers if we get to chose where to place the experience point?

from the documentation:

Coaches

Coaches will give a boost to players training based on their specialty. For this boost to work you must set the specific training type for each player. You can only use a specific training type if you have the right coach. The default training type is "General", it enables to skill up any skill but its slower than specific training.

List of skills that each training type will enable to level up.

0 general - any skill but slower
1 Goalkeeping - handling
2 Defending - off the ball, positioning, tackling, heading, set-pieces
3 Attacking - off the ball, positioning, heading, finishing, set-pieces
4 Technique - passing, technique
5 Physical - strength, speed, natural fitness