The answer, as in many UX situations, is "It depends."
But seriously, it sounds like:
- there are some areas of the system in which the Cancel button and the Remove button do different things, and need to be differentiated from each other.
- there are some areas of the system in which they do pretty much the same thing.
First, we'd need to find out whether it is necessary to have both buttons present in all situations.
If not, then having the right buttons there in the right circumstances will be helpful.
Second, if the difference isn't clear, we can often look to copy or visual placement to clarify the differing roles of these buttons. Some approaches may be:
renaming the buttons - it may be that "Cancel" and "Remove" aren't the right names for these buttons. You can look at other names that would clarify their difference, or look at providing help copy that clarifies their difference. But in choosing this approach, remember that, as a general rule, if you're writing too much copy to explain how something works, there's probably something wrong with the design that should be remedied first.
placing the buttons close to the things they act on. If the buttons tend to work on things close to them, the placement can help clarify the difference between them.
There are other approaches that can be helpful, too. These are general approaches that can help frame the problem for you. If this doesn't help, just come back and provide some screen shots and examples so we can give you more specific feedback.