Dun is the Gaelic form and it's British cognate is Din as in Denbigh (cf Dun beag). Caer, I believe is derived from the Latin 'caster', hence it's appearance in place names where there has been a Roman fortress, eg Cramond, Caer (Chester).

Edinburgh was a din in the time of the Votadini (y Gododdin) but as I said, in Modern Welsh it has become Caeredin.