musk
odoriferous reddish-brown substance secreted by the male musk deer (dried and used in medicinal preparations and as a perfume), late 14c., from Old French musc (13c.) and directly from Medieval Latin muscus, from Late Greek moskhos, from Persian mushk, from Sanskrit muska-s "testicle," from mus "mouse" (so called, presumably, for resemblance; see muscle). The deer gland was thought to resemble a scrotum. German has Moschus, from a Medieval Latin form of the Late Greek word. Spanish has almizcle, from Arabic al misk "the musk," from Persian.
The musk-deer, the small ruminant of central Asia that produces the substance, is so called from 1680s. The name musk was applied to various plants and animals of similar smell, such as the Arctic musk-ox (1744). Musk-melon "the common melon" (1570s) probably originally was an oriental melon with a musky smell, the name transferred by error [OED]. Also compare Muscovy.
muscle
"contractible animal tissue consisting of bundles of fibers," late 14c., "a muscle of the body," from Latin musculus "a muscle," literally "a little mouse," diminutive of mus "mouse" (see mouse (n.)).
So called because the shape and movement of some muscles (notably biceps) were thought to resemble mice. The analogy was made in Greek, too, where mys is both "mouse" and "muscle," and its combining form gives the medical prefix myo-. Compare also Old Church Slavonic mysi "mouse," mysica "arm;" German Maus "mouse; muscle," Arabic 'adalah "muscle," 'adal "field mouse;" Cornish logodenfer "calf of the leg," literally "mouse of the leg." In Middle English, lacerte, from the Latin word for "lizard," also was used as a word for a muscle.
Musclez & lacertez bene one selfe þing, Bot þe muscle is said to þe fourme of mouse & lacert to þe fourme of a lizard. [Guy de Chauliac, "Grande Chirurgie," c. 1425]
Hence muscular and mousy are relatives, and a Middle English word for "muscular" was lacertous, "lizardy." Figurative sense of "muscle, strength, brawn" is by 1850; that of "force, violence, threat of violence" is 1930, American English. Muscle car "hot rod" is from 1969.
mouse
Middle English mous, from Old English mus "small rodent," also "muscle of the arm" (compare muscle (n.)); from Proto-Germanic *mus (source also of Old Norse, Old Frisian, Middle Dutch, Danish, Swedish mus, Dutch muis, German Maus "mouse"), from PIE *mus-, the old Indo-European name of the mouse, retained in several language families (source also of Sanskrit mus "mouse, rat," Old Persian mush "mouse," Old Church Slavonic mysu, Latin mus, Lithuanian muse "mouse," Greek mys "mouse, muscle").
Plural form mice (Old English mys) shows effects of i-mutation. As a type of something timid or weak, from late 14c. Contrasted with man (n.) from 1620s (nor man nor mouse). Meaning "black eye" (or other discolored lump on the body) is from 1842. Computer sense of "small device moved by the hand over a flat surface to maneuver a cursor or arrow on a display screen" is from 1965, though the word was applied to other things resembling a mouse in shape since 1750, mainly in nautical use.