Pseudo-crypto-quasi-neo-saturated

Like heat transport mechanisms, different sorts of atmospheres can be confusing, so a comparative list might be helpful. One practical consequence of the physical differences is different lapse rates (in the presence of gravity, downward temperature slopes). Another is that the relationship among temperature, pressure, and density profiles is different.*

(Dry) adiabatic atmosphere. This is the simple case given in all the basic textbooks: heat energy (proportional to temperature) declining with altitude, as gravitational potential energy increases. It's adiabatic because no heat is being added from or removed to the outside.

This atmosphere is steady in time and has no matter or energy flows traversing it. Each layer satisfies local thermodynamic equilibrium (LTE).

(Wet) saturated adiabatic atmosphere. This is a more complicated case. The heat released by condensation of water vapor shallows the downward temperature slope. The action of gravity in converting heat energy to potential energy is still at work, however. The temperature still falls with altitude, just not as fast.

If you take wet air as a unit (water and dry air together), this atmosphere is still adiabatic. No heat is exchanged with the outside. The atmosphere is still steady, and there are no matter or energy flows. LTE is satisfied mechanically (pressure up against gravity down) and thermally (local temperature). Phase equilibrium is satisfied where water liquid and vapor are in equilibrium (in the clouds), although the ratio of liquid (or crystal) to vapor changes with altitude.

Pseudoadiabatic atmosphere, saturated or not. This is the most complex case. The atmosphere is steady, but there are now steady energy and possibly matter flows as "through-put." In practice, the energy flows are convective or radiative or both; the matter flows are water diffusing up as vapor and occasionally precipitating down as drops or crystrals.

At each layer, LTE is satisfied completely if there is phase equilibrium, as in clouds. (In the clear air, phase equilibrium is violated.) But because of the flows, this atmosphere cannot be called adiabatic. The LTE condition has to be supplemented by a list of the flows and the relevant boundary conditions on them, either at the surface or at the atmospheric top.

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There's a funny Greek or Latin name for everything in physics - including physics, from the Greek physis, meaning "change" or "growth" - roughly what we call "evolution" today, used in a very broad way. In thermodynamics, fluid processes can be labeled by what remains constant, using the prefix iso- meaning "same." Isothermal means constant temperature (Greek therme for heat); isobaric means constant pressure (Greek baros for pressure); isochoric means constant volume (Greek choros for space); and isentropic means no change in entropy (Greek entropos for "turning inside"). Adiabatic comes from a-diabatos, not pass-through-able.

So what do we call a pseudoadiabatic atmosphere, one with LTE and steady flows? (BTW, pseudos in Greek means fake or mistaken. ) A cute adjective I thought of comes from the Greek rheos, for flow (as in rheostat) - we'll call it isorheoic.
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* For experts: this is difference between different effective polytropic exponents connecting pressure and density, respectively, to temperature. For the dry adiabatic atmosphere, it's 7/5 (ratio of specific heats); for the actual pseudoadiabatic atmosphere, it's just shy of 5/4.