Those wire clamp headlight bulb mounts aren’t unique to Hyundai. I have them in a Toyota Corolla and a Subaru Legacy GT wagon. It’s apparently the new way, less weight and less cost.
Yea, same in my '95 Honda Del sol. Tried replacing my first headlamp bulb after 190,000 miles and it was a bitch. I don't think I got the wire clamp on properly but the coupling that attaches to the back of the bulb holds it in place perfectly fine.........