"Turing Complete" refers to a system which can be configured to be come any Turing Machine. When we write a particular program in some language and run it on some input, we have a Turing Machine. If the language lets us create any Turing Machine (i.e. do any Turing computation), then it is a Universal Turing Machine, and Turing Complete.
Turing's Tape Machine is a UTM because the tape can be initialized with contents to turn it into any TM. Any calculation for which there is a TM can be done by the UTM (if someone can figure out what to put on the tape).
Turing's Tape Machine is a UTM because the tape can be initialized with contents to turn it into any TM. Any calculation for which there is a TM can be done by the UTM (if someone can figure out what to put on the tape).