All, yes.
Keep in mind it is an equivalent, not necessarily a real resistance that can be pinned on any particular aspect of the component.
For example, an ideal capacitor in parallel with a resistor, will measure some (finite nonzero) ESR, at some frequency. (In fact there is even a formula for this conversion.) Even though there is literally no resistor in series with the capacitor.
Clearly, when we say "ESR", we're not saying "this explains how the component works/is" -- we're saying "this component looks like this [at some frequency]". That last bit is often implied, but crucial: an equivalent is only true at one frequency.
In an electrolytic capacitor, its electrolyte is an obvious aspect, that has significant resistance, and which appears in series with the component. We might expect that "ESR" measures this resistance. In fact, at the capacitor's minimum frequency point (typically somewhere in the 10kHz-1MHz range, depending on value), the resistance is indeed mostly due to the electrolyte. But if we measure at a low frequency, the ESR is higher -- so it seems this does not capture the full picture.
So there are different kinds of equivalents.
Suppose we have an AC impedance meter, measuring at some frequency. It measures some amount of resistance, and some amount of reactance. We can express it as a series or parallel equivalent, just as well (thanks to the conversion formula). The meter has no way to know whether it should express its result one way or another: which way is more representative of the circuit, or more useful to the operator.
So, often, such meters have selectable outputs, so you can get the readout in terms of resistance, in series or parallel with, capacitance or inductance. (Indeed, if you select the wrong one, you might get a negative inductance, say -- and rightfully so, as a capacitor can be seen as a negative inductance at a given frequency!)
A more advanced kind of equivalent, is the equivalent circuit. As it happens, for most capacitors, the C + ESR + ESL circuit gives modest accuracy (say within 10%), over a practical frequency range (say kHz to MHz). We can accomplish a lot of real work, just using this simple model! It's still not a complete picture of a capacitor, but it gets us a lot closer, and it seems to be "more correct" than our alternatives.
Tim