Routine can be used as a noun, adjective, or verb (although it's quite rare and probably best avoided).
Courtesy of Oxford Dictionaries:
- NOUN: a sequence of actions regularly followed; a fixed program.
- ADJECTIVE: performed as part of a regular procedure rather than for a special reason.
- VERB: to organize according to a routine.
When "loop" is used as a noun it suggests one or more steps (a routine) that are repeated. "Repeat", used as a noun, would refer to an event that is like some previous event, but not necessarily planned or fixed (like a routine would be). "Loop", used as a verb, suggests returning to the starting point or step and "repeat", used as a verb, suggests doing something (like a routine) again.
So the words are related, but only "loop" and "repeat" are common as verbs and both imply repetition (where routine does not). The only substitution I've heard would be "loop" (noun) and "routine" (noun). (e.g. "John completed his daily loop." or "John completed his daily routine.")