Dyed film gets its darkness from organic dye suspended in adhesive. UV breaks those dye molecules down. Blue and green pigments degrade first, the red survives longest, and about three summers in, you're looking at a purple rear window and a bubbling edge.
Carbon film replaces the dye with carbon particles, which don't fade — the color is structural, not chemical. Ceramic film goes further and uses nano-ceramic particles that reject infrared energy specifically, which is the part of sunlight you actually feel as heat on your arm.
3M has been in this material for a long time. They invented reflective window film in 1966 and multilayer optical film in 1998 — the same class of engineered thin-film stacks used for thermal management in aerospace applications. The reason a modern ceramic film can be light in appearance and still cool a cabin is that it's rejecting a band of energy your eye can't see.
The old metalized films solved fade a different way, with a sputtered metal layer. They worked, and they also interfered with GPS, tire-pressure sensors and cell reception, and eventually corroded to bronze. Nobody should be installing those on a modern vehicle.
The practical version: pay once for carbon or ceramic, or pay three times for dyed.