No, not the same.
Cooldown is the time to reuse the same skill.
While the delay is the waiting time to use some skill. In short, the Delay blocks you use any skill until finished.
Example.
Storm Gust have 5 sec Delay.
You can not use any skills until the end of the delay (the delay is calculated to match the animation of the effect of Storm Gust).
Asura have:
Cast: 1 sec
Delay: 1 sec
Fixed-Cast: 1 sec
Cooldown: 0 sec