English inherited mouse through Germanic. Latin independently made musculus, “little mouse,” for a moving muscle beneath the skin; its feminine form was also applied to the shellfish. English later borrowed both Latin descendants and eventually respelled the shellfish as mussel.
Sources: Online Etymology Dictionary, mouse, muscle, and mussel; Merriam-Webster, “Muscle & Mussel.”
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Dates follow the earliest cited evidence for the form and sense shown. Notes name the sources. Timeline spacing is compressed; undated stages are placed in sequence.