The 'old' term names were introduced at the Scottish Universities in, I think, 1911. They refer to the traditional Scottish 'quarter days'. Quarter days are different in England, and the historic terms at Oxbridge, the Inns of Court, some schools etc. were originally (4) quarters.
http://en.wikipedia.org/wiki/Quarter_days
At St Andrews, there was some attempt to have it both ways in the mid-90s. Term and semester dates were listed in the calendar, but terms have since fallen by the wayside. The semesters are still officially called 'Martinmas' and 'Candlemas', though.
Incidentally, a semester is the period of six months (two half-sessions in a 12-month year, not all of which need be teaching time). Our 'semesters' should be called 'half sessions', not semesters.
In my view, the problem with the current system is that it leaves far too little time to prepare for the second 'semester' (for both students and staff). Exams should be held in May; or, at the very least, Sem 1 exams held before Christmas. But the academic year would have to start so early then that the University would miss out on holiday, conference and golfing revenue from Halls. That's why it didn't happen in 1994.