What is a quadrangle called that has 2 pairs of equal sides but is not a parallelogram?

Only a kite would qualify under the terms set. The kite is a shape similar to a rhombus, except that two adjoining sides are of equal length, and the other two adjoining sides are not the same...

draw a kite

Rhombus Actually a rhombus is in the parallelogram family, it just is a special member.

A kite shape is one example -- 2 long sides adjacent to each other & 2 short sides adjacent to each other.

its a kite