It's all about the undertones with these two colors. Alabaster is warmer than Snowbound, with more beige undertones than gray. Snowbound is brighter, Alabaster is creamier.
BM Pure White’s LRV (Light Reflective Value) is 80.88, so it’s a bit darker than Snowbound. The undertones are much cooler, bending more toward a gray than a greige or even beige color.