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An enumerator is defined as a 7-tuple: https://en.wikipedia.org/wiki/Enumerator_(computer_science)

A Deterministic Turing machine is defined as a 7-tuple: https://en.wikipedia.org/wiki/Turing_machine

How are these definitions different? Can a DTM M simulate an enumerator E, for part of its computation can it call an enumerator E as a subroutine and run it to some point then do something with its output etc?

I assume the answer is yes, you can do things like enum in normal programming with universal language / universal machine. Since DTM is usual definition of universal machine it can perform an enumeration-- just want to be sure, maybe I'm wrong and its a fundamentally different kind of machine?

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Yes. A deterministic Turing machine can simulate another deterministic Turing machine (possibly only up to some point), and an Enumerator is a particular kind of deterministic Turing machine.

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