Phasors are complex numbers. They are scalars, although we can also define them in terms of magnitude and angle on the complex plane.
Vectors are vectors. Vectors have both magnitude and direction.
While either one can be defined by two real numbers, they are not the same.
As far as EE goes, the main difference between them is the multiplication operator that applies.
When you multiply two complex numbers (phasors, for example) you get a product with a magnitude equal to the product of the magnitudes of the multiplicand and the multiplier, and an angle that is equal to the sum of the angles of the multiplicand and the multiplier.
When you multiply two vectors, you must choose (depending on the problem you're trying to solve) either scalar multiplication (dot product) or vector multiplication (cross product).
If you choose (or require) the dot product, you get a product with magnitude equal to the projection of the multiplcand onto the multiplier, and with no angle at all---the product isn't even a vector, it's a scalar.
If you choose (or require) the cross product, you get a product with a magnitude equal to the product of the two operands' magnitudes times the sine of the angle between them. And with a direction perpendicular to both of the operands (thus, not even in the vector space defined by the two operands).