RAE is the Research Assessment Exercise rating. This takes place every 5 or 6 years (the last one was in 2001) and determines the level of research funding a department will receive until the next RAE. The top mark is 5* (some departments refer to a Double 5*, which means they have received the top rating twice running).
The TQA (Teaching Quality Assessment) last took place in 1998. We continue to use it here as shorthand for government measures of teaching quality and student support. Reports on teaching quality are currently carried out by the QAA (Quality Assurance Agency). Systems for England, Scotland, Wales and Northern Ireland vary and subject specific ratings are not always available.