You Do Need power plug adapter while traveling from Spain to Vatican City.

Here is Why You Need An Adapter

The outlet and plug type used in Vatican City are C, F and L and in Spain are C and F. This is how they look like.

Spain

In Spain, outlets of type C and F are in use.

Type C

Type F

Vatican City

In Vatican City, outlets of type C, F and L are in use.

Type C

Type F

Type L