Bonsai are generally planted in soil that's specifically blended for the particular sort of bonsai species. Special for bonsaiBonsai soils of the same soil type may be packaged in different sizes of granules, eg 0.5cm or 1.5cm etc, and some bonsai soils aren't granular: they have different compositions etc. The same type of soil may have different Romanisations of the original name. But they are soils. Often the soil for a tree will be a blending of several of the specialised soils, cf simply using one kind only, and at the bottom something with a coarser consistency for drainage & aereation.
They are small trees, and their environments are small, yet complete. There may be some specimens which are grown hydroponically, but generally bonsai are grown in soil, soil which often consists of of a blend of more than one specialised bonsai soil component, and with some coarser soil/ gravel at the bottom. Also, some trees simply don't do well unless in well drained soil. Often the soil would be different from vegetable soil, but might contain eg 25% vegetable soil in the blend. Also, bonsai soil needs to be replaced every several years so that the soil will continue to be able to provide micronutrients which the bonsai draw from the soil. Bonsai generally aren't special cases of hydroponics.