Is there a food that is halfway between a cheesecake and regular cake? While living in Korea, there was one special bakery I found that had a cake that I can only describe as being halfway between cheesecake and regular cake. It was creamy like a cheesecake, but had a density somewhere between an actual cheesecake and the airy texture of a regular out-of-the-box cake.

It had the wonderful flavor of a cheesecake, but was lighter and fluffier. I would love to bake something like this so I can try it again. Is there a name for such a cake?

The dessert looked like cake from the outside: it had tiny holes everywhere, albeit smaller than what you would see in a regular cake. It was also shaped into a loaf, and the top would rise a bit. It was more dense than a regular out-of-the-box cake, and definitely had a flavor similar to cheesecake. I would have called it a "cheesecake flavored cake" at first impression. It also had a bounce to it, if I pressed it down, it would bounce back up to a degree.
Perhaps you're looking for the soufflé cheesecake, which has a moderate amount of flour in it. This style is also popular in Japan.

The other style popular in Japan is the "rare cheesecake", which is set with gelatin instead of being baked. I think this is probably denser than what you're referring to, so I left it out of my first edit, but worth considering if the soufflé style doesn't match your expectations.

In Germany, some quark cheesecakes have flour in them as well, and those often have a more sturdy texture with a bit more air than the New York style.