Spinebot gave good info, use Import Project
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Note you can have multiple skeletons in the same project. That can save you some jumping back and forth between projects.
In general copying your animations isn't great, as now you have to keep them in sync if they change. Same with having 2 skeletons that are similar, if you change one you may need to change the other. What happens when you have 3-4 skeletons or animations? Or a dozen, or a hundred?
You could use skin bones and constraints to combine multiple characters into a single skeleton. For example, an angle skin could have wing bones. This scales better to having many characters, or characters that are highly customizable.
That said, if you truly have different skeletons that don't share bone setup or animations, then using a separate skeleton makes sense.