Hi Guys -The difference is quite simple, a 180 degree appraisal is usually the person themselves and their manager filling in a questionnaire = 2 dimensions. 270 degree is self, manager and peers = 3 dimensions, 360 is self, manager, peers and the direct reports of the person = 4 dimensions.
Then as you add extra dimensions such as stakeholders, customers, etc... it just keeps adding another dimension.... So in essence a 360 degree appraisal is identical in process terms to a 720 - it just has additional relationship groups.
270 is mostly used at the top and bottom of organisations, the top where lets say the director CEO actually has no boss - so its self, peers and direct reports.
At the bottom where the people do not manage any others - so it's self, peers and manager.
From our experience 540 degree is mostly used where it is an internal function supplying another part of the organisation - so you end up with: self, manager, peers, direct reports (and either customers - or stakeholders).
One of the critical considerations is that when other groups are used there are at least 2 members (e.g. direct reports or stakeholders) that way they are slightly better 'protected' and therefore more likely to 'say what they think'.
Have a look at my site - there are several free download documents that should answer your questions about this type of process.
http://www.reactive360.com