Is frictional force and gravitational force are the same?

No, they are different things.

Frictional force is the force which arises when to bodies are in contact.

Gravitational force is the force attracting matter and matter, and doesn't require contact.

No. A frictional force is the force when two bodies are in contact. Where as the gravitational force is the attraction of the matter by the earth.

Not quite. It is also gravitational force which attracts the Earth to the Sun, and it's also gravitational force which attracts Jupiter to the Sun. So, you should not restrict gravitational force only to the Earth.