A bath generally is any space that has plumbing and some fixture for personal hygeine. There is debate as to what consitutes a full bath, 3/4 bath, half bath etc. and I have found this varies from region to region and MLS to MLS. A full bath generally has a tub/shower, sink, and toilet. Some will say a 3/4 bath is a shower, sink, and toilet. Others will say that is also a full bath. In larger homes the bathroom may be a suite comprised of a tub room or shower room, a lavatory ( a room with a toilet), a sink room, also a space for a spa, hot tub, steam room, sauna. A powder room would be a room attached to a bath suite, or a master suite which would not necessarily have any plumbing.