Within the Editor window (and to some extent within the Mixer window too), there are several techniques for deleting objects (regions, control points, and more).

Using the mouse and keyboard

Select the object(s) and then press the Del key. This does not put the deleted object(s) into the cut buffer, so they cannot be pasted elsewhere.

Using normal cut and paste shortcuts

Select the object(s) and then press x. This puts the deleted object(s) into the cut buffer so that they could be pasted elsewhere.

Using just the mouse

By default, Shift Right will delete the clicked-upon object. Like the Del key, this does not put the deleted object(s) into the cut buffer.

The modifier and mouse button used for this can be controlled via Edit > Preferences > User Interaction > Delete using .... Any modifier and mouse button combination can be used.