Are "gas phase" calculations the same as "vacuum" calculations?
I don't know the etymology of the phrase, but yes, "gas phase" calculations are the same as "vacuum" calculations. There is no difference.

Think of it this way: the only option other than a "gas phase" calculation is one where solvent is included, either as explicit atoms or implicitly via a mathematical model or even a solid-state/bulk-model calculation. This indicates that the solute is in the gas phase, and hypothetically not interacting with the environment in any way.