Does the adjective "different" have a comparative form? If so what is it?
There's no single word, no.
Different has three syllables, and English adjectives of three or more syllables (as pronounced, not spelled) must use the periphrastic more or most to form a comparative or superlative phrase.
The comparative suffix -er and superlative suffix -est can only inflect adjectives of one syllable, with a few -- mostly ones ending in /i/ or /o/ -- of two syllables swinging both ways.
- big: bigger, biggest, *more big, *most big
- easy: easier, easiest, ?more easy, ??most easy
- narrow: narrower, narrowest, more narrow, ?most narrow
- helpful: *helpfuller, *helpfullest, more helpful, most helpful
- interesting: *interestinger, *interestingest, more interesting, most interesting
Just one more example of dying inflections in English. There are only 9 inflectional suffixes in English, and this is two of them, both hanging on only in common monosyllables.