Consider an inductor in the real world it is a coil of wire and this wire has resistance distributed along its entire length.
The best model is therefore to consider a tiny inductor in series followed by a tiny resistor and this is repeated infinitely many times such that if you were to add up all the inductances you get the total inductance. Similarly if you add up all the resistances you get the ESR (Equivalent Series Resistance).
You therefore can never measure the inductor voltage or the resistor voltage because there is no point in the circuit to measure it. We can only measure \$ V_R + V_L \$.
Mathematically we can model this as a single inductor in series with a single resistor. For almost all cases this is good enough; only if we are trying to model the H and E fields around a component to we need any more detail.
The voltage across the ideal single inductor \$ V_L \$ and the ideal single resistor \$ V_R \$ will be different and frequency dependant.
We must not confuse this with the AC impedance however \$ X_L = 2 \cdot \pi \cdot f \cdot L = \omega \cdot L \$. This is sometimes modelled as a resistor but does not account for the \$ 90^o \$ phase shift.