Are hydrogen oxygen and water the same?

Short answer: Yes.

Technically correct answer: Depends on the water. Hydrogen is an element defined by having 1 proton. However elements can have different numbers of neutrons and still be the same element, but be a different isotope. 'Normal' hydrogen is called protium and has no neutrons. If it has 1 proton it's deuterium, and 2 tritium. These occur naturally but in low amounts, and can be found in water. If the concentration of deuterium is high its called heavy water. So in this sense, not all the hydrogen atoms would be the same; there would be 3 types (more than 3 protons is unstable on only produced in a lab, and won't last long)

Depending on question: if you were actually asking "are the hydrogen atoms in water identical to the hydrogen atoms you find in other molecules?" Then yes (taking into account isotopes, the profound atoms in water molecules are the same as elsewhere). That is to say, they are interchangable.

Note: Only their nuculei would be identical, what the electrons get up to will be different, but the important thing is they are interchangeable.