What's the difference between "kha " and "k͟ha"?
I can't figure out the difference. How do they differ in pronunciation (if they do)?
'kha'(ख) is the aspirated version of 'ka' (क) while 'k͟ha'(ख़) is a letter that's borrowed from Arabic/Persian and is used mainly in loanwords from these languages. 'k͟ha' must be correctly pronounced as the 'ch' sound in the Scottish 'loch' (or the ach-laut in German).
That said, most Hindi speakers do not make the distinction and pronounce 'k͟ha' as 'kha'. It is also common to use ख instead of ख़ in writing. This is probably why the audio that this course uses does not make the distinction. Urdu, Hindi's sister language, is written in the Persian alphabet which uses different letters for 'k͟ha' and 'kha' and so, they are always seen as distinct there.
kha is more like sound of bad /bæd/ sound of 'æ' in bad and k͟ha is sound of father /ˈfɑːðə(r)/ sound of 'ɑː' in father. You can also distinguish
this in script by opening this page and type kha and a drop-down menu will appear first word is k͟ha written as (खा) and third word is kha written as (ख ) in Devangari Script.