Question

How does the composition of a mixture of hydrogen and oxygen differ from the composition of a compound containing hydrogen and oxygen

Answer 1

Chemical compounds have chemically bonded molecules so that they exhibit different properties (i.e. chemical) compared to the individual molecules comprising the compound. Mixtures are simply the combinations of different molecules and compounds that are not chemically bonded together, and can therefore be separated by physical means. Mixtures usually retain the properties of its components. 

The hydrogen and oxygen molecules in a mixture do not form strong bonds between each other. The molecules of both gases are only contained in the same space or volume and the individual molecules retain their chemical properties. 

A compound containing hydrogen and oxygen molecules exhibit different chemical (and even physical) properties compared to the individual molecules themselves.

Water for example, is a compound with 2 hydrogen atoms and 1 oxygen atom, chemically-bonded together. Hydrogen gas is highly flammable, water is not. Oxygen gas is an essential reagent for combustion (or burning) reactions, water is not. 
 
Thus, throwing a lighted match to a gaseous mixture of hydrogen $(H_{2})$ and oxygen $(O_{2})$ would create fire, or even an explosion (since hydrogen is flammable and oxygen feeds the reaction). Throwing a match to water vapor $(H_{2}O)$ would not create fire.