I also find this to be confusing. However, I think that theWikipedia "Quantum State" explanation of the difference is less confusing than the Wikipedia "Density matrix" explanation.
It states that the mathematical difference between the two is that the trace of the density matrix of a pure state is 1, but the trace of the density matrix of a non-pure mixed state is less than one.

The issues of first preparing and second measuring pure versus non-pure mixed states adds further complexity.

I also find this to be confusing. However, I think that the Wikipedia "Quantum State" explanation of the difference is less confusing than the Wikipedia "Density matrix" explanation.
It states that the mathematical difference between the two is that the trace of the density matrix of a pure state is 1, but the trace of the density matrix of a non-pure mixed state is less than one.

The issues of first preparing and second measuring pure versus non-pure mixed states adds further complexity.

The quantum superposition can be a pure state, but I think you can also prepare mixtures of two different quantum superpositions,