FCs allow their members to buy a private room. This is an instanced space about the same size as a room at the inn, or about the same size as a single floor of a small house. So yes, it is an apartment.

You have complete authority of how you can customize this room, including furniture, flooring, walls, and lights. You can also make the room public and allow fc members or friends to visit.

If you leave the FC, or are kicked out, you lose the room and all furniture in it must be retrieved from the housing npc in the residential proper. You do not get a refund for the 400k you spent to buy the room, however you do get your furniture. Just be sure you have enough inventory room to carry it.