Can a data set have records from multiple objects?

No, you cannot have records from two different objects in the same data set.

Think of the data sets like views. You can only have views for one object at a time, and the same is true of data sets.

The workaround is having two data sets on the map at once. You do this by running your first search, selecting your next data set, unchecking Clear Map on Search, and running your new search. Both results will be layered on top of each other on the map and available in the list below.