attack speed is referred to the speed with which you do the attack, for example if you have high attack speed, when pressing whatever buttons you press to attack from maybe a 2 seconds delay it goes to like under 1 second, which is good especially in pvp since you get to hit more, cause if you can hit every second, in one minute you can attack 60 times instead of 30, so its very good
meanwhile cooldown is kinda the thing used to equilibrate attack speed, after attacks you get a cooldown which means you cant use the same attack again until a N of time has passed, for example you attack and then theres a 2 seconds cooldown, so even if you have high attack speed you cant use that attack again, but still with attack speed you can use another attack which should still be as fast, so you kinda use the combo, attack1 attack2 so in between the cooldowns you attack another way.
anyways this is like a general games explanation, i havent really paid attention to the storys game, hope this was useful anyways and excuse my shitty explanation
What's the difference between cooldown and attack speed?