What is the difference between half controlled and full controlled rectifier?
A Half-controlled rectifier, when it comes to power circuits, is typically a bridge rectifier that uses two SCR's and two diodes for a single phase bridge, and 3 SCR's and 3 diodes for a three phase bridge..  This was common a long time ago, when SCR's were much more expensive than diodes.

By the same token, a full-controlled rectifier uses SCR's for all control elements; 4 in a single phase bridge, 6 in a three phase bridge.

Edit to add (per comment below): A half controlled rectifier (full bridge) can only control power flow in a single quadrant, the first.  Full controlled rectifiers can control power in quadrants 1 and 2.  More, if you add a second bridge for 4 quadrant control, you must have a fully controlled bridge, as one has to be completely turned off when the other is firing.