Do you know why hexagonal lattice and hcp structure are different?

hcp contains two atoms essentially one at the position 000 and the other at position 2/3,1/3,1/2. It is essential that we have these two points to construct the unit cell and hence one atom at 000 is the lattice point and the other at 2/3,1/3,1/2 is a basis. Hence hcp is a structure and hexagonal lattice does not have the basis point and it is simply called a hexagonal lattice..

I feel more understanding from my part is needed here to explain things still.

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