Basic difference is in the composition. One group made up of silicates and the other are all other minerals.

Silica and oxygen are the two most abundant elements in the crust constituting about 74% of the crust. Minerals containing silicates are silicates and others are non silicates. The silicate minerals constitute about 90% of the total minerals. Non silicate minerals are oxides, sulfides, halides, carbonates, native elements etc