Is there an established distinction between a geyser and a cryovolcano in solar system bodies?
An educated guess: on Earth, the working fluid in a "geyser" is water, which remains a fluid more or less permanently after each eruption.  This means that geyser eruptions are not associated with buildup of new geological material around the geyser (apart from the much slower process of dissolved minerals accumulating as the water evaporates).

Contrariwise, on Earth, the working fluid in a "volcano" is molten rock, which solidifies after reaching the surface.  Each new eruption permanently deposits new solid material in the vicinity of the volcano.

If I were writing definitions, I would define a "cryovolcano" as a geological vent system where the working fluid is water, but where the environment is cold enough that the ejecta from eruptions accumulates in a permanent mountain of ice around the vent.