How are logo'd t-shirts printed?

Depends on how you define small. I have a friend that has a t-shirt company and there is a point where it is cheaper to make a screen and go from there. If you need ten it is cheaper for the inkjet but if you need a few hundred having a silkscreen made is cheaper depending on how many layers you need.

Do the inkjet methods print directly on the t-shirt? I think they print onto a transfer material that will be ironed onto the t-shirt.
As @johnpowell mentions for any larger quantities screen printing is used for all sorts of reasons including durability of the printing, easy availability of screen-printing machines and facilities and ultimately, cost-effectiveness.