Phasor vs Vector vs Space Vector
A vector is a mathematical entity that we all know and love; it's a \$1 \times N\$ matrix of numbers that indicates a position in \$N\$ dimensional space.

A phasor, as @ThePhoton pointed out, isn't really a vector.  It's a lot like a vector, but it's really a complex number denoting a sinusoidal current or voltage at some reference frequency that's had the reference frequency component removed.  Thus, you can do arithmetic on it using complex number rules, not vector rules.

When you say "space vector" I believe you're talking about "space vector modulation".  I'm really not sure where the space vector is in space vector modulation, but I suspect that for the time being, you'll confuse yourself by thinking too hard about the "vector" part.