These two transfer paper types have two totally different functions. "Clear" transfer paper is for white or light gray fabrics and "opaque" transfer paper is for colored fabrics.
The prints you can re-produce from inkjet printers are translucent or "see-through". Since the inks are expected to be printed onto a white background, they can use the white from the paper to re-produce the correct colors. Transfer paper is either opaque or clear for this reason.
Clear papers can be used on white or light gray because the color of the garment will add white (or gray) to the ink colors and make them show up correctly.
Clear papers are thinner and usually less expensive than opaque papers can be.
Opaque papers can be put onto any color fabric because the transfer paper will provide the white needed to correct the colors you print.
Opaque papers are usually more expensive than clear paper and slightly thicker to block out the color of the farbric.
What happens if you put clear papers on a colored fabric? If you put a printed clear paper designed for whites onto a green shirt, all of the colors you printed will have added green in them which is not what you printed.
Bottom line: Use clear papers when you can, opaque papers when you have to!