Lighting design design expert with 7 years experience here. That's what we usually refer to as a 4" can with rotating lens. Existing fixture is very cheap and has little to no photometric design for creating a a desirable spectograph/spread. It's the equivalent of a wide spread flashlight in your ceiling.

To replace it, buy any LED can that fits in the hole, buy a goof ring (look it up in regards to drywall/construction/lighting) and make sure that the unit itself is rated for straight line voltage. You want to make sure that the driver for the LED is included and pre-wired to take standard voltages.

I sugges using prolighting.com, 1000bulbs.com, or something similar. They will be more expensive than what you find at home depot, but many of their offerings are used by businesses because of their cost versus life value.

If I was you, I'd install a new can that accepts e26 or e27 screw in lamps and then buy a box of LED par30 lamps so you don't need to replace the fixture if it goes.