A control relay is a "magnetic switch" which can isolate a circuit, so is in effect the same as a "breaker". An "exciter breaker" and an "exciter control relay" are in effect the same thing.
An exciter breaker (exciter control relay) will isolate the power to the voltage regulator.
The generator breaker will isolate the generator from the bus bar.
The tie breaker will isolate two different bus bars from each other, or can connect two generators to the same bus bar.
In most cases you will want to keep bus bars connected so that you can use all your services, so you will trip the generator breaker to isolate the generator from the bus bar, and the exciter breaker so you effectively shut down that generator.
If you have 2 generators supplying the same single bus bar then you will trip the tie breaker to isolate generator and the generator and exciter breakers to isolate and shut down the generator.