I have tried it three times, and that seem to the case: the CP and HP are different because the two players are at different levels and one Pokemon has a low CP like 10 or 14, and the other Pokemon has a high CP such as 384.
But if I check for the IV and Perfection of the CP 384 Pokemon, it gave me one number, and if I spend stardust and candies to power up the CP 10 Pokemon, I do get the same Perfection number as the other player's Pokemon.
So are they the same Pokemon with the identical IV and Perfection number? If that is the case, one way we can save stardust and candies is to catch 2 or 3 Pokemons by 3 players, and then just run through the IV calculator using "Calculate" for the first Pokemon, and use "Refine" for the other 2 Pokemons. Then in this case, we may be able to save stardust which sometimes would be 3000 or 3500 stardust.