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

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