[doctoring]

Rituximab is a monoclonal antibody which targets a B cell surface protein, CD20. Monoclonal antibodies are pretty cool, in that we've figured out how to make a thing that our bodies normally make, and engineer versions that target specific items we want. Antibodies binding to things can alter their function, disable them, and/or cause them to die. In the case of rituximab and CD20, through a variety of antibody-mediated mechanisms, the attached antibodies in effect causes the B cells to die off.

CAR-T cells, on the other hand, is essentially making a fairly small (but kind of insidious) modification to T cells in the lab. These T cells when put back in the body then do their normal T cell thing and proliferate and recruit more of the immune system, but to try to eliminate a target you've chosen for them. The most useful/successful target thus far has been CD19, another B cell surface protein.