Energy generators generate energy from power stations, and transfer this energy to supply grids. Energy suppliers purchase energy from energy generators on the supply grid, and sell it on to consumers. Energy suppliers operate in a competitive market and consumers can pick their energy supplier.
Energy price caps are limits placed on the unit cost of electricity and gas that an 'energy supplier' can charge a consumer/household. Energy suppliers continue to purchase energy from 'energy generators' in the wholesale market at market prices. The energy suppliers are compensated by governments for the price difference.