What are similarities and differences of primitive cells and unit cells? 

Ans:  Unit  cell  is  the  basic  building  block  of  a  crystal,  repeated  infinitely  in  three dimensions.

It's characterized by the three vectors (a, b, c) that form edges of a parallelopiped and the angles between the vectors (alpha, angle between b and c; beta, the angle between a and c; gamma, angle between a and b).

A primitive cell is a unit cell built on the basis vectors of a primitive basis of direct lattice, namely a crystallographic basis of the vector lattice L such that each lattice vector t of L may be obtained as an integral linear combination of basis vectors, a,  b,  c. It comprise only one lattice point and its volume is equal to the triple scalar product (a, b, c).

Non-primitive bases are used usually to illustrate centered lattices. In that case, unit cell is a multiple cell and it contains more than one lattice point. Multiplicity of the cell is given by the ratio of its volume to volume of a primitive cell.