The Sega CD doesn't have sprites, nor does it have a graphics chip. It has an ASIC, a chip which manipulates memory. All the drawing is still being done by the Sega Genesis. The Sega CD itself is seen by the Sega Genesis as though it was a game cartridge inserted and addressed in RAM. The Sega CD has two 128kb memory buffers, and a switch. When the switch is in one way, the Sega Genesis sees one of the banks, as though it was a cartridge, and the Sega CD sees the other, as RAM. The Sega CD can freely write to that 128kb bank in any way it wants, independently of the Sega Genesis. The Sega CD has it's own 68000 processor and an ASIC to accomplish all this. The Sega CD also has it's own VRAM.
The Sega CD doesn't work with background layers or sprites or any of that. It has a buffer it can write to, in any way it wants. Think of it like opening a new file in paint. It can paste stuff around, stretch it, scale it, etc. It can do this over and over again, pasting new stuff on top of old stuff. How it arranges the frame is however it decides. It could make the frame buffer a sprite sheet, like this:
Or it could draw a complete, complex scene on the frame buffer, like it's doing in Soul Star, where the entire screen is being rendered this way.
Once it's done with it's buffer, it can flip the switch, and the Genesis can see this as though it were a cart. The Genesis can then load the graphics in memory on the "cart" that is the Sega CD, as though it were loading graphics off of a cartridge, into VRAM. Once in VRAM, it can treat the art just like any other tiles. It can use them to build a sprite, or it can use them as background tiles one on of its planes. The Sega CD's memory can also provide nametables for the planes, so it can arrange the tiles back into a full screen image. This double buffering system lets the Sega CD stream data, albeit at a lower framerate. This is how it does things like Sonic CD's special stages.
In fact, however, because the Sega CD's memory was treated like a frame buffer, it wasn't limited to Mode 7 stuff like the SNES was. It could have honestly done things like Galaxy Force II, albeit at a much lower scale.