Only some are, eg John Downie. But many are not, in particular the European wild crab is not. Many Malus species can be called crab apples, and we cultivate several of those species, eg, M floribunda, M sieboldii, and a number of crosses, eg M x robusta, as crabs. It used to be thought that the domestic apple was descended from Malus sylvestris, the European wild crab apple, and many of the crabs we grow are cultivars or crosses of M sylvestris. But it is now known the cultivated apple is derived the rare central Asian species Malus sieversii found growing in eastern Kazakhstan and adjacent areas of China.