Answer
Yes, there definitely is a difference between a homogeneous mixture of hydrogen and oxygen in a 2:1 mole ratio and a sample of water vapor.
A homogeneous mixture of hydrogen and oxygen in a 2:1 mole ratio contains separate molecules of hydrogen and oxygen in the 2:1 ratio.
Hydrogen can be separated from oxygen.
Whereas in a sample of water vapor, the hydrogen and oxygen are bonded with each other to form a chemical compound. Thus hydrogen and oxygen cannot be separated from each other via physical means.
Work Step by Step
Explanation already provided in answer, but in short:
Homogeneous mixture of hydrogen and oxygen has separate, different molecules of both of them, which are not chemically bonded. The mixture can be separated into its constituents.
Whereas in water vapor, the hydrogen atoms are chemically bonded with the oxygen atoms.
