As I understand it, the basis is the group of atoms whilst the primitive unit cell is the unit space that fits the total space without any gaps, and only containing one lattice point? How do the two relate to each other? Thanks.
They don't relate.
The primitive unitcell is a property of the lattice. The lattice has nothing to do with the basis. You can have a single atomic basis or a thousand atomic basis but both have the same lattice, and therefore the same primitive unit cell.
One of the most important facts you have to wrap your head around is that a lattice point has nothing to do with an atom. A lattice point just defines the origin of a local coordinate system. The position of the basis atoms is defined in this local coordinate system.