I'm getting a bit confused on the difference between reaction wheels and momentum wheels.
Reaction wheel and momentum wheel are near synonyms. Manufacturers of reaction wheels / momentum wheels (e.g., Collins Aerospace; other manufacturers are similar) typically do not distinguish between the two because the same device can be used for both purposes.
The distinction between the two lies in how the wheel is used. Reaction wheels have a nominal rotation rate that is zero or nearly zero. The small rotation rates means that multiple reaction wheels act nearly independently. Momentum wheels on the other hand have a nominal rotation rate that is markedly non-zero. The large rotation rate adds off-axis stability to the spacecraft, but with the added complication of interactions between momentum wheels. In both use cases, the wheel's rotation axis is fixed with respect to the vehicle, and angular momentum is transferred between the spacecraft proper and the wheel by changing the wheel's rotation rate.
As mentioned in the other answer, control moment gyros (CMGs) represent yet another way of controlling spacecraft attitude using rotating parts. CMGs rotate at a nearly constant and very high speed, typically much higher than a momentum wheel's nominal rotation rate, and the rotation axis is not fixed with respect to the vehicle. CMGs take full advantage of the weirdness of rotational behavior: Pushing on a rotating object in a direction orthogonal to the rotational axis results in a torque in the third orthogonal direction. Because CMGs operate at very high rotation rates, the torque that results from a small orthogonal push can be very large.
CMGs however come at a rather large cost compared to reaction / momentum wheels. The very high rotation rate requires extremely precise manufacturing to avoid the unbalanced washing machine syndrome. That the rotation rate is supposed to be constant requires precise controllers and sensors. That the rotation axis is not fixed requires even more sophistication. These added complexities result in CMGs only being used on very large spacecraft such as the International Space Station.