The shark family that includes the great white, mako, and porbeagle sharks is Lamnidae.
Lamnidae is the family of mackerel sharks, a group of powerful, generally cold-water predators. Its living members include the great white shark, Carcharodon carcharias; the shortfin and longfin makos, Isurus oxyrinchus and Isurus paucus; and the porbeagle, Lamna nasus. These species share a streamlined body, pointed snout, large gill openings, and prominent teeth.
The family name comes from Lamna, a Greek word associated with a predatory fish and linked to the mythological Lamia. Lamnid sharks are famous for speed and active hunting. Great whites and makos also belong to the order Lamniformes, but that broader rank includes other families and sharks such as the goblin and megamouth sharks.
That family-versus-order distinction is the main trap in this question. Lamnidae is not synonymous with all mackerel sharks: “mackerel shark” can describe the entire order Lamniformes or, in narrower usage, members of Lamnidae. The great white is the largest and most famous member, while makos are especially noted for speed.