Slab is a type of foundation consisting of a structural concrete slab poured directly on the grade. No accessible space exists in slab construction.
Slab foundations are popular in areas (i.e. the Southern United States) where there is a relatively high water table (i.e. the “water table” refers to the depth in the soil at which you find water). Traditionally, the slab foundation is normally the least expensive foundation type when building on a relatively flat lot.
Crawlspace is a type of foundation which includes an accessible space with limited headroom, typically between the soil and the bottom of the first floor of a home.
Crawlspace construction is predominant in areas where there is heavy clay content in the soil, where the home owner needs additional under-home storage space, or the homeowner needs access to pipes, wiring, etc. under the floor of the home.
Basement is a type of foundation which includes an accessible space between the soil and the bottom of the first floor of a home. It usually has more headroom than a Crawlspace.
Basement foundation construction is predominant in cold climates where the foundation needs to be situated below the frost level.
Best wishes in the building of your new home!