discreet

1325–75; Middle English discret < Anglo-French, Old French < Medieval Latin discrētus, Latin: separated (past participle of discernere; see discern), equivalent to dis- dis-¹ + crē- separate, distinguish (variant stem of cernere) + -tus past participle suffix

1. See careful.

Discreet, meaning “judicious, prudent, modest,” comes partly from Middle French discret “prudent, discerning,” used in Anglo-French in the sense “wise person.” The Latin source was discrētus, past participle of the verb discernere “to separate, distinguish, mark off, show differences between.” In Late Latin discrētus also acquired the sense “prudent, wise,” possibly arising from association with the noun discrētiō, which shows a similar semantic development: physical separation to discernment to capacity to discern.
Discrete, “apart or detached from others; separate; distinct,” was originally a spelling doublet of discreet, sharing meanings and both deriving from the same Latin source. The spelling discrete is closer in form to Latin discrētus and is probably an attempt to differentiate discreet from discrete.
The Middle English Dictionary has two senses at the headword discrēt(e): the sense “wise, morally discerning, prudent, circumspect” has 29 citations; the sense “separate, distinct” has four (in angelology, astronomy, and mathematics).
It wasn’t until the late 16th century that discrete became restricted to its present meanings, leaving the spelling discreet to predominate in its own current uses.