The question can look obscure, but it isn't. Complex impedance is a way to present how certain measurable quantities depend of each other in a certain system in certain conditions. It's a physical quantity as well as complex phasors of current and voltage are physical quantities. These all are defined in circuit theory.
Voltage and current (sinusoidal or other) present things which are considered to be a part of lower level physical theory (=electrodynamics) than the circuit theory. Circuit theory is an abstraction which hides such things as what current and voltage are. In circuit theory we formulate concepts "sinusoidal voltages and currents" and present them with complex phasors. In circuit theory we assume that resistors, capacitors and inductors obey certain equations that bind voltage and current to depend on each other. Those equations we have got from electrodynamics. We can prove a circuit theory fact: Complex impedance presents how sinusoidal voltage and current depend on each other.
Difference: Complex phasors of voltages and currents are built in circuit theory on voltage and current which are defined in electrodynamics. Complex impedance is built on concepts which are defined purely in circuit theory, but it's still a physical quantity and can be measured.