Is there a difference between a homogenouos mixture of hydrogen gas and oxygen gas, and a sample of vapor? explain?

Yes. In a homogeneous mixture the hydrogen and oxygen are not chemically combined; in water vapor, they are. You can separate a homogeneous mixture of hydrogen and oxygen by physical means, such as by cooling the mixture until the oxygen liquefies. If you cool water vapor you're just going to get liquid water and then ice - not two separate substances. That's because compounds can only be separated into their elements by chemical means.

The density would be 1.622