1) Nothing you can do in wordpress (to my knowledge) will allow you to change abc.com to widgets.com. And from a networking standpoint this is like asking for the same phone number as burger king’s phone number – impossible. You’d have to contact hostgator to see if they’ll allow a domain name change to a DIFFERENT domain (see first sentence).
2) They may also have an free option within the control panel to forward your name (IE when someone hits abc.com the URL will show as abc.com/widgets). This option is pretty common.
There are ways to perform the latter in wordpress (or so I’m told – I’m trying to figure this out myself) but that’s not what you’ve asked in your post.