Discrete, from Dictionary.com:
[dih-skreet]
–adjective
1.
apart or detached from others; separate; distinct: six discrete parts.
2.
consisting of or characterized by distinct or individual parts; discontinuous.
3.
Mathematics .
a.
(of a topology or topological space) having the property that every subset is an open set.
b.
defined only for an isolated set of points: a discrete variable.
c.
using only arithmetic and algebra; not involving calculus: discrete methods.
Discrete would be used in a sentence as follows:
The supervisor made it clear to her employee, who was also her lover, that job performance and sexual performance were discrete matters.
Discreet, from Dictionary.com:
[dih-skreet]
–adjective
1.
judicious in one's conduct or speech, esp. with regard to respecting privacy or maintaining silence about something of a delicate nature; prudent; circumspect.
2.
showing prudence and circumspection; decorous: a discreet silence.
3.
modestly unobtrusive; unostentatious: a discreet, finely wrought gold necklace.
Discreet would be used in a sentence as follows:
The supervisor and her employee kept their affair discreet.