For my opinion, the terms "voltage series" or "current series" are somewhat confusing because it is not inicated what is (a) the controlling quantity and what is the controlled quantity.
Hence, I prefer expressions like "voltage controlled voltage feedback" (which, for example, applies to non-inverting opamp circuits).
In the actual case of an emitter follower it is the voltage developped at the emitter node which causes the feedback. Because this feedback voltage is caused by the emitter current we can say that the common collector configuration (emitter follower) realizes "current-controlled voltage feedback". This is true for both cases you have mentioned - DC feedback and ac feedback.
However, because in both cases the emitter current(s) and the effective resistances are different the feedback factor differs also.