The projective-space tag is---according to the description---about the space of lines through the origin in some vector space in geometry, so every geometric question that relates to $\mathbb{C}P^n$ or $\mathbb{R}P^n$ belongs there. No matter whether it's algebraic geometry, differential geometry, geometric topology, .... In particular, as already suggested by others, when you're asking a question about projective space in its incarnation as algebraic variety, use the algebraic-geometry tag first and then this one.
The projective-geometry tag, however, is rather concerned with this kind of geometry. (It's the projective counter part to Euclidean geometry in the classical sense.) Therefore, a question about projective space as a model for projective geometry could tag both, projective-geometry and projective-space, but a question about desargues' theorem, e.g., may only tag projective-geometry but not necessarily projective-space.