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Water is made of 2 hydrogen atoms and 1 oxygen atom. Hydrogen peroxide is made of 2 hydrogen atoms and 2 oxygen atoms. As water and hydrogen peroxide are made of the same types of atoms, they can be considered as similar substances

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AL2006

No. Chemical compounds are seldom similar to the elements they're made of.

Here is another example to think about:

Sodium . . .
a soft, silvery-white, highly reactive metal;
If exposed to air, the surface rapidly tarnishes and turns dark.
It reacts with water, to the point that a large piece in water may explode.

Chlorine . . .
a pale yellow-green gas at room temperature;
a strong bleach and disinfectant;
in the upper atmosphere, responsible for ozone depletion;
extremely dangerous and poisonous for all living organisms;
used in World War I as the first chemical warfare agent;
 
Chemical compound of sodium and chlorine . . .
not a highly reactive metal
does not tarnish and turn dark when exposed to air
does not explode in water
not pale yellow-green
not a gas at room temperature
not useful for bleach or disinfectant
not responsible for ozone depletion
not dangerous or poisonous for living organisms
never used as a chemical warfare agent
chemical name:  "sodium chloride"
common name:  "salt"
widely used in cooking and eating, to season food