Heater is inside the Cathode (white coated thingy), next is the grid (can be more than one), and then the plate (anode).
Rectifiers are basically the same but dont have a grid, though you can use a triode as a rectifier if you tie the grid to the plate.
Then there are directly heated triodes (DHT) where the heater is the Cathode.
I think that second tube is a beam tetrode, where the inner plate helps direct the electrons to the plate. There is also two grids inside there, one bring a grid and the other being a screen. That's about all i know about them.