Alternate definitions of enumeration machines
Multitape machines are equivalent to single tape machines. You can simulate several tapes on a single tape. In particular, in order to simulate the "print state" model using the "write-only output tape" model, you simulate an extra output tape, and whenever the print state is reached, you copy the contents of the extra output tape to the write-only output tape. Therefore both models are equivalent.

More generally, all reasonable Turing machine models are equivalent. This is a special case of the Church–Turing hypothesis.