Regatta

in a Regatta two or more crews race head to head (i.e. at the same time). Often they consist of a series of races, involving heats, leading (eventually!) to a final. It is usually only the winning crew from the final (of each event) that receives an award (tankards, medals or otherwise).
This is the kind of race featured in the Olympics and the famous Oxford vs. Cambridge 'Boat Race'.

Head

in a Head Race crews compete on a time trial basis. In this all the crews competing race at once in convoy (although large events may split this into two or three sections in order to make it easier to manage and allow for boat sharing). Again, it is usually only the winning crew from a particular event that receives an award.

Indoor

in an Indoor event each person races (on a rowing machine) a set distance (usually 2000 meters), each trying to get a faster time than everyone else in their event. These events are not as common as the other two mentioned and therefore we enter just one per year - the North of England Indoor Championships.
However, occasionally, members of the club have entered the National Indoor Championships - where world records are often broken!
Indoor rowing events are entered by many health clubs, police forces and companies, as you don't necessarily need to know how to row/scull in order to use a rowing machine properly, and therefore the competition at these events is often different (usually greater) to that met at actual boat races.