Quarks are said to have no internal structure, however there are many types of quarks. On the face it would seem that they are defined by properties (Mass, Spin, Charge), how do we differentiate between properties and structure when many properties are defined by particles?

They have isospin, strangeness, charm, topness and bottomness. Basically, when new quarks were identified, we tagged them with whatever property it is that differentiate them from up and down quarks.

There's also color, which enters into their interactions. 

No structure means they are not composite particles.

Quarks and electrons and photons all have completely different properties but they are all elementary / fundamental particles and, hence, have no internal structure.