I have done a lot of searches on the types of momentum wheels, but I couldn't find too much answers. What are the differences between a Bias Momentum Wheel and Reactive Momentum Wheel, and what they are used for? It is really hard to find a topic on these on the internet.
It might be that the problem arises from terminology: there is no term "Reactive Momentum Wheel" in common use. The following terms are actually used:
This has an average speed of zero, it can spin up positive or negative around zero in response to torques around the orbit. The zero average speed means of course that its contribution to angular momentum is also zero on average.
This has a finite average speed. Typically it could be run at several thousand r.p.m though the speed is also controllable and it can vary its speed in response to torques around the orbit. The constant average speed leads to the term "momentum bias" also being used in this situation.
In principle both roles of reaction wheel and momentum wheel could be achieved with the same hardware and some satellites actually have wheels that can be reassigned to either mode. See here: Can a reaction wheel be spun up using an external torque and be used as a momentum wheel?
"What are they used for"
This is harder to answer in a simple terms as they form a part of the attitude control subsystem and the design of that is where the decision is made. Basically the choice of whether to have a momentum biased mission or a 3 degree-of-freedom design will depend upon the range of attitude manoeuvres required, the attitude stability desired and the precision and availability of other potential components in the system such as attitude sensors, actuators (thrusters), and other causes of disturbance (slosh, flexible appendages).
Key point: a momentum biased satellite is gyroscopically stabilised, i.e. its spin axis is well defined. The whole point is that it takes a bigger disturbance torque to perturb its attitude than in the unbiased case.