VF-17 was one of the first two US Navy Corsair Squadrons. It was briefly put aboard the USS Bunker Hill in 1943, at the tail end of Corsair carrier trials, but pulled right back off when it was decided to assign Corsairs to land duty. VF-17 then became a Navy land based Corsair unit.

Navy squadron VF-84 was formed on 1 May, 1944, from a nucleus of VF-17 veterans, and flew the Corsair from the Bunker Hill as part of Air Group 84. They served aboard her with Marine squadrons
VMF-221 & VMF-241. Late in 1944, the Navy wanted Corsairs on its carriers, but it had very few of its own squadrons with that aircraft. So, USMC Corsair squadrons were put aboard in numbers to supplement, as Michael Potter notes below.

Aboard USS Wasp (CV-18) USMC squadrons VMF-216 & 217 were the primary Corsair operators, along with Navy squadron VBF-86. The VBF squadrons are a topic by themselves:

https://en.wikipedia.org/wiki/VBF

https://en.wikipedia.org/wiki/VBF-1

From this site:

https://www.wings-aviation.ch/25-Navy-Sqn/VBF-Squadrons/083/VBF-83.htm

This quote:

"The Bomber Fighter Squadrons, were created to reduce the Fighter Squadrons in an Air Group to an acceptable size. Fighter Squadrons had up to 60 planes and 100 pilots. Normaly a Fighter Squadron was split in two to creat a Bomber Fighter Squadron."

My now deceased friend Ed Dill was a divebomber pilot through WWII. He told me a story of one admiral (I don't recall who) that was so disgusted by the Helldiver (Ed hated it, too) that he ordered them out of his force. According to Ed, the Corsair made an excellent divebomber, and they were then substituted. Again as Michael Potter notes below, Essex got rid of her Helldivers for Corsairs. Navy VBF-83 served on Essex with USMC VMF-124 and 213 in Air Group 83. I think I am here seeing confirmation of Ed's account to me.

The Navy did put its own Corsair squadrons into carrier service late in the war. However, there were few of them, so they served aboard with USMC squadrons.