The RPG Makers have their tile sets broken up into uniform segments, so you can select tiles and draw with them in the editor. This reduces your game size, as you're using the same tiles over and over in different parts of the map - the image only needs to be saved once, in one location, and the code "stamps" it everywhere it needs to go.
Parallax mapping is the opposite - you don't use tilesets at all (or very much), but you create an image the same size as your map and you actually draw your map at full size using an image editing program. Then you use a script to put it into the game. The tiles you see in the editor are usually just used for blank tiles that have the appropriate passage settings (though some people use a script and regions, so they don't use tiles at all).
They take much longer to create, take much more space on the disk, but can be much more stunning to view and play.
