If a BMS, has more amps than the battery requires, what effect does it have on the system?
The battery doesn't require amps. It has the capability to supply a certain amount of them, and this shoudln't be exceeded, or it will stress the cells or damage them.
The BMS is there to protect the battery from this kind of overload (and from overvoltage and undervoltage, which also stresses or damages the cells).
The controller has to supply the motor with the power the motor demands to overcome the conditions it's pushing against, and all that power comes from the battery.
So the battery, both cells and BMS, must be able to supply it. That means you must size the battery and the BMS to be fully capable of handling the worst-case demands of the controller (which in turn must be able to supply the worst case demands of the motor under your specific riding conditions and usage).
The controller has a current limit to protect it's own hardware and the battery. Cheap ones are a fixed limit on the battery side. more advanced ones may be user-alterable limit, and some have both battery and motor current limits; the only one that matters for this discussion is the battery current limit.
Usually you size the battery and BMS to handle everything the motor/controller will ever need, and so the controller current limit is set to what the system will require to do the job you want it to do.
If you haven't worked out what all of that is and just get or already have a battery your'e just going to use anyway, then you set the controller current limit to below what the least-capable part of the battery is (cells or BMS or interconnects, etc), to prevent damage to the battery.