Caster Classes usually have cast times, some skills are instants like healing, dispelling or the basic attacking skills for example.
Melee Classes usually have animation, each skill "hits" the opponent differently, eg. Skill A wings the sword and attacks the enemy on the left, Skill B makes the character jump and hit the enemy from above.
Skill animations usually dont last longer than a second and usually have a cooldown, depending on each skill. Powerful skills will have a longer cooldown.