a vector has threetwo elements usually a direction and magnitude. Normally it points to a position in an N dimension space from another point, most of the time this other point is the origin so it just points to a position.
a phasor is a convenient way to express an imaginary number pair R+jX where R and X are the real and imaginary components respectively and j is \$ sqrt{-1}\$ as a module and an angle related to the origin.
now space vectors is not like a phasor or a vector even, it is a convenient way of showing an inverter scheme(make AC voltage from DC) for three phase systems. You got three rows of where you have DC voltage so you have you can call them ABC, you can connect each as plus or minus with switches so you got \$A_+ B_+ C_+\$ and \$A_- B_- C_-\$ now the vectors just indicate who is on and who is off as a state, but ultimately you are talking about multiple DC voltages being turned on and off, there are some rules to it.
simulate this circuit – Schematic created using CircuitLab
So no, a phasor and space vector(modulation) are not the same thing but they can be closely related.