I use Windows. Yes, the cursor changes.

Referring to the Table which DaveRo linked to on 23 May 23 - 05:42 PM

General - default is the main cursor - it looks like the outline of an arrow.

Internet link - Links and status - looks like a pointing hand when I hover over a link

Selection - text is in the text box (cursor looks like "I")

Drag and drop - grab - looks like a grabbing hand when I grab and move e.g. Google map to move to the location I am interested in.