Question

Are physical quantities and dimensions the same thing?

Answer 1

No.
The dimension of the units of a derived physical quantity may be defined as the number of times the fundamental units of mass, length and time appear in the physical quantity. The expression for velocity obtained above is said to be its dimensional formula. Thus, the dimensional formula for velocity is [M⁰ L T ^–1].

In the above example, velocity is the physical quantity and [M⁰ L T ^–1] is the dimension of that physical quantity.