Theorem. Turing machines with semi-infinite tape are equivalent to standard Turing machines.
An off-line Turing machine has two tapes. One tape is read-only and contains the input; the other is read-write and is initially blank.
Theorem. Off-line Turing machines are equivalent to standard Turing machines.
A multitape Turing machine has a finite number of tapes, each with it's own independently controlled tape head.
Theorem. Multitape Turing machines are equivalent to standard Turing machines.
A nondeterministic Turing machine is one in which the dfa controlling the tape is replaced with an nfa.
Theorem. Nondeterministic Turing machines are equivalent to standard Turing machines.