Is "passenger loading bridge" a synonym to "contact stand"?
ICAO Annex 14, which deals with aerodrome design (not really terminals) uses the terms PLB and aerobridge.

Wikipedia lists many names for it, with the official being PBB (Passenger Boarding Bridge). The names listed are jet bridge, jetway ®, gangway, aerobridge/airbridge, air jetty, portal, and skybridge.

Official FAA documents use the term PBB. (Example.)

Contact stand most probably is used to distinguish it from a remote stand, it's not very popular according to Google. Rotunda or pivot describes that a PBB pivots, or perhaps the pivoting / telescoping part.

To answer the main question, yes they all mean the same thing, with PBB being an official name.