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Basement is a type of foundation which includes an accessible space between the soil and the bottom of the first floor of a home.

Source: houseplangallery.com

Block foundations use cinder blocks (8 x 8 x 16 inches) that are stacked on each other and cemented in place with mortar. The process starts on the top of the footings with each row forming its own course. The blocks are then reinforced with rebar placed vertically in the holes or cells and filled with concrete

*Block foundation typically indicates a basement or crawlspace foundation

Source: bobvilla.com

Is a slab on grade or slab on ground can be many different styles. in this case it is referring to a conventional foundation (a house foundation reinforced with rebar instead of post tension cables), sitting on top of piers. It is the same as a Slab inspection.

Source: Link to definition

A builder's warranty, which may be backed by the builder or by a third-party warranty company, usually comes in two parts — a workmanship and materials warranty and a structural warranty.

Source: builderpeople.com

A builder's warranty inspection is a thorough inspection of your newly constructed home that you order before the warranty expires. Most builders provide a 12-month warranty that covers defects with workmanship and materials.

Source: aahomeinspection.net