We really aren't a Tileset is the graphics, and can be used on many tilemaps.. The tilemap is the "grid" of tiledata (which tile to draw). Tilesets (like a grass/ground/path graphic set) will be used over and over again in different levels etc. just like a sprite, it's reused a lot.
Tilemaps as I said are is the grid of tile data. If you have a 32x64 tilemap then this is basically a "grid" of INT values. Each INT has a few bits for flags, and some of the bits for the TILE index itself. But its just an int.
So.... Tilemaps are full of tile data, and Tilemaps will use a Tileset to render with - just like a sprite.