I have one object that has the “screw” modifier. When I join it to another object it gives that object the screw modifier too. I even tried with the Boolean modifier, but it doesn’t let me move both objects at the same time.
If moving the objects together is the only concern, try parenting them by using Object (Keep Transform) option in the parenting context menu that you can open with Ctrl+p. You select child object first and then the parent object. You can delete this parent-child relationship by opening Clear Parent menu by pressing Alt+p and selecting Clear Parent option.