CSI _ ok am confused now

[Saltire]

I thought that all the CSI's in all the CSI shows - vegas, NY and miami were police officers.
But in an episode I watched tonight of CSI vegas, grissom said to a suspect " we are crime scene investigators, not police officers(or he might have said not detectives)", yet in CSI NY, Mac Taylor is called Det Taylor, and curly sue is Det Bonasera. So they are clearly police offciers.
Confused

He said not detectives. But I agree, makes very little sense to me.

Doesn't matter, I love 'em all!!

I haven't watched CSI Miami in a while so not sure if they are all police/detectives or just CSIs. Well, Horatio Sunglasses is a Lt not sure about the others