On what basis would you classify energy sources as
$(a)$ renewable and non-renewable?
$(b)$ exhaustible and inexhaustible?
Are the options given in $(a)$ and $(b)$ the same?

(A) The source of energy that replenishes in nature is known as a renewable source of energy. Sun,wind,moving water,and biomass are some examples of renewable sources of energy.
The source of energy that does not replenish in nature is known as a non-renewable source of energy. Coal,petroleum,and natural gas are some examples of non-renewable sources of energy.
$(b)$ Exhaustible sources are those sources of energy that will deplete and exhaust after a few hundred years. Coal and petroleum are examples of exhaustible sources of energy.
Inexhaustible sources of energy are those that will not exhaust in the future. These are unlimited. Solar energy and wind energy are examples of inexhaustible sources of energy.
Yes,the categories given in $(a)$ and $(b)$ are essentially the same.