Important to note that native speakers would refer to the stretchy ice cream as "dovme dondurma", which roughly translates to "beaten ice cream".
The distinction seems to be:
> Two qualities distinguish Turkish ice cream: hard texture and resistance to melting, brought about by inclusion of the thickening agents salep, a flour made from the root of the early purple orchid, and mastic, a resin that imparts chewiness.[citation needed]
> The Kahramanmaraş region is known for maraş dondurması, a variety which contains distinctly more salep than usual. Tough and sticky, it is sometimes eaten with a knife and fork.[citation needed]
I'm a native speaker, I think it depends on the region. But yeah, "dövme dondurma" is more specific. The part I'm from did not make the distinction, however.
The distinction seems to be: > Two qualities distinguish Turkish ice cream: hard texture and resistance to melting, brought about by inclusion of the thickening agents salep, a flour made from the root of the early purple orchid, and mastic, a resin that imparts chewiness.[citation needed]
> The Kahramanmaraş region is known for maraş dondurması, a variety which contains distinctly more salep than usual. Tough and sticky, it is sometimes eaten with a knife and fork.[citation needed]