rut (n.1) Look up rut at Dictionary.com
"track," 1570s, probably from Middle English route (see route); though OED finds this "improbable." Metaphoric meaning "narrow, monotonous routine" first attested 1839.
rut (n.2) Look up rut at Dictionary.com
"animal mating season" (originally of deer), early 15c., from Old French rut, ruit, from Late Latin rutigum (nominative rugitus) "a bellowing," from past participle of Latin rugire "to bellow." The verb is recorded from 1620s. Related: Rutting.