Meaning of "Discretion"

They both carry the same basic sense of discernment or judgement which can be considered synonyms of the word.

Discretion derives from the Latin stem discrēt- meaning to separate or to divide - and therefore to discern (which is also derived from the common stem cernĕre (to separate)) - giving rise to two words in English which essentially mean the same (discreet and discrete). Thus, to be discrete means to separate or divide, which means to be discreet or to exercise discretion (discernment). The spelling discreet tends to be used more in a moral context with the second spelling discrete now more common in other contexts.

Here are the two senses as defined in OED. The sense of "choice" is related to the English word discrete, while the sense of "care" is related to the English word discreet.

I. [ < ancient Latin sense of discrētio.] 4.a Liberty or power of deciding, or of acting according to one's own judgement or as one thinks fit; uncontrolled power of disposal.

III. [Compare discreet adj., adv., and n.] 6. a. Ability to discern or distinguish what is right, befitting, or advisable, esp. as regards one's own conduct or action; the quality of being discreet; discernment; prudence, sagacity, circumspection, sound judgement.

The example you give could be read either way. "Practice discretion" could be a euphemism for "act without consulting your supervisor" or it could mean simply that you are discreet.