The grip for the CZ 24 looks different to me than that for the CZ 27.
The CZ 22 was a Mauser design made under license:

.
The CZ 24 was a Czechoslovak design, but an apparent refinement of the CZ 22:

.
The CZ 27 is a further refinement:

.
Looks like all three models have wrap-around grips, but the more refined the model, the curvier the grip?
Is the 27 substantially thinner than the 82? With half the capacity in .32 Auto, I would think so.