Yeah I think you've been a bit confused with the various forms of diffusion.
This is what I've gathered so far this year:
Carrier-mediated (also called FACILITATED DIFFUSION):
Involves protein channels AND carrier molecules, no energy expenditure, from high conc. to low conc.
Channel-mediated:
Involves protein channels (NO CARRIER MOLECULES NEEDED), no energy expenditure, from high conc. to low conc.
Now any form of diffusion across a membrane THAT DOES NOT REQUIRE ENERGY is deemed PASSIVE transport, and so both channel- and carrier-mediated forms of transport are forms of PASSIVE TRANSPORT.
Active transport:
Involves protein channels (NO CARRIER MOLECULES), it DOES REQUIRE ENERGY EXPENDITURE, from low conc. to high conc.
All energy-requiring forms of diffusion are deemed ACTIVE forms of transport and so active transport is deemed an ACTIVE form of diffusion (as its name suggests!)
Hope that helped..