1. Tuning $S$ is equivalent to tuning the representation of SU(2), i.e. one considers spin-1/2 [spin operators represented by $2 \times 2$ matrices], spin-1  [spin operators represented by $3 \times 3$ matrices], spin-3/2  [spin operators represented by $4 \times 4$ matrices] , etc.
Tuning $N$ takes us away from SU(2) to SU(N) spins. Mathematically, a key difference between the two semi classical limits, therefore, arises in terms of the number of generators: while spin-S has 3 generators (irrespective of the value of S), SU(N) has $N^2-1$ generators.

2. CP(N-1) is a specific kind of SU(N) generalization in that it is the coset space of a special pattern of SU(N) symmetry breaking where SU(N) $\to$ U(N-1) [this generalizes the more familiar pattern of (internal) symmetry breaking that one encounters in magnetism which corresponds to the case N=2]. Therefore, they are inequivalent large $N$ limits.