Well Abr stands for Area border router. Area 0 is a very special area in ospf which has the capability of sharing inter area routes. Abr is some thing in which at least one of its interface is connected to area 0. If incase you are not able to connect to area 0 physically you can do so logically by using the concept of ospf virtual link. 

Asbr stands for autonomous system boundary router when ever you perform redistribution by using commands like redistribute connected subnets (to redistribute the connected subnets to that router) then that router is called as asbr.