mode (n.1)

"manner;" late 14c., "melodies, strains of music" (a sense now obsolete; see musical senses below), from Old French mode and directly from Latin modus "measure, extent, quantity; proper measure, rhythm, song; a way, manner, fashion, style" (in Late Latin also "mood" in grammar and logic), from PIE root *med- "take appropriate measures."

Meaning "manner of acting or doing, was in which a thing is done" is by 1660s. Sense of "inflectional category in conjugation" is mid-15c. In music, 1670s as "method of dividing the intervals of the octave for melodic purposes" in reference to ancient Greek music; by 1721 in reference to modern music.

mode (n.2)

"current fashion, prevailing style," 1640s, from French mode "manner, fashion, style" (15c.), a specialized use of the French word that also yielded mode (n.1).

Definitions of mode

mode (n.)
how something is done or how it happens;
their nomadic mode of existence
Synonyms: manner / style / way / fashion
mode (n.)
a particular functioning condition or arrangement;
switched from keyboard to voice mode
mode (n.)
a classification of propositions on the basis of whether they claim necessity or possibility or impossibility;
Synonyms: modality
mode (n.)
verb inflections that express how the action or state is conceived by the speaker;
Synonyms: mood / modality
mode (n.)
any of various fixed orders of the various diatonic notes within an octave;
Synonyms: musical mode
mode (n.)
the most frequent value of a random variable;
Synonyms: modal value