What you're seeing is dynamic tile parallax. A lot of PCE games use it. Dracula X, for example... in MANY places, but most notably in the first part of Stage 6... those blue bricks in the background that move slower than the rest of the level... dynamic tiles. And it's easy for games like that which rarely scroll on both axes... when you deal with dual scrolling, it's a whole new ball game... required memory for two-dimensional dynamic parallax will be no less than 3x that of one-dimensional dynamic parallax... and that's to say nothing if you have a complex design which requires an entire tile scroll... that equates to 8x the memory required. And if you have such a complex pattern, you're already going to be using 8 unique tiles for horizontal alone... you then need 7 more variant sets of 8 tiles each. That's 64 unique tiles... and that's only for *one* repeating pattern... imagine if you have several independent scrolling tiles (like Dracula X does). Now, each of these dynamic tiles tile consumes 1KB of RAM. However, in a game like this one, tiles are represented as *metatiles*, which means that everything has now expanded to 4x the usage. Again, this is also dependent on the complexity of your tiles. In my demo, only four tiles are required to pull off the parallax, and since it's a solid up-down pattern, it could go vertical without even noticing that there's no actual vertical parallax.
Another thing Dracula X does, which is also seen in quite a few other games (like Air Zonk) is h-int parallax. Basically, what you're doing here is redrawing parts of the screen based on the position of the raster. That's how you get games with serious full-line parallax. Air Zonk nailed this one *hard*, as did Shadow Of The Beast. My platformer currently doesn't show off this technique, but it will later on. Of course, some games combine both techniques in the same display, and then you can also mix sprites into the display to give the illusion of "true" parallax by creating "uneven" scrolls.
So yeah, anyways... you do dynamic tile parallax when you want to create areas where the background is simple but you need a complex foreground arrangement, and you use h-ints for when your foreground is simpler but you need complex backgrounds with full-line parallax scrolling.