Is Ahri a poke mage or an assassin?

She's a kiting mage and an assassin

If we want to put it in the terms that Riot came up with last year, she's closer to a mobile Burst Mage. She doesn't quite have the range of an Artillery/Poke Mage (think Xerath, Ziggs), but doesn't have Syndra's or Veigar's burst. So instead, she kites and chases as needed.

As far as I know, Ahri is an AP jack of all trades champion; she has everything, but none to a "specialized" extent. Some sustain, some (completely dodge-able) poke and some burst, a single target skill shot CC, and some mobility. She doesn't have Vlad's or Swain's sustain. She doesn't have Xerath's poke. She doesn't have Syndra's burst. She doesn't have Zyra's CC (much less control of the field). And she certainly doesn't have Katarina's mobility.

jack of all trades

She's a ranged melee tanky DPS assassin mage tank support jungler. She excels at everything.

ahri is a "kite" mage

she is able to do poke or assassinations as well