In equestrian jumping events, are the fences in the same pattern for every event or do horses (and riders) need to adapt to new courses every time?

They are all different. For Cross-country events, that is obvious, as they are on different courses, which conform to the terrain. For stadium jumping, each event is set up to conform to the requirements of the group organising the event, and the level of the competition. The higher the competition, the tougher the course. At a local club competition, many riders will be able to produce a clear round. At the Olympics, the course is often so tough that nobody manages it. When a competition has multiple rounds, the course will (at the higher levels) usually be changed between rounds.

Grand Prix is the uppermost level of show jumping. It runs under International Federation for Equestrian Sports (FEI) rules. In this type of horse show jumping, the horse jumps a course of 10 to 16 obstacles, with heights up to 1.6 meters (5 feet 3 inches) and spreads of up to 2.0 meters (6 ft 7 in).

https://www.happycomlysporthorses.com/how-to-become-a-grand-prix-rider/

Edited to add that, if you watch the Olympics or other Grand Prix events on television, you will hear the commentators discussing the design of the course, and naming the person responsible for it. Riders get a chance to walk the course, inspecting the fences and making plans for the way they will approach them, before the competition.