What is the difference between .sage and .sagesw?

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First, note that the endings are .sage and .sagews. The first is just a text file written in the Sage language (i.e. Python + syntactic sugar + Sage commands), whereas the second is a file specifically for SageMathCloud/CoCalc use only. (There is also a .sws format which is from the old sagenb notebook.)

So load with .sage is using it exactly as intended - for instance, you could define a new function my_func in that file, and then loading would make my_func available for use in your session. But .sagews is a "Sage worksheet" in the CoCalc environment, and it doesn't make sense to "load" a whole worksheet in that sense, though one could presumably convert it to a file that could be loaded.