Difference between the prefixes "pre" and "ante"?

From New Oxford American Dictionary

ante- PREFIX
before, preceding
pre- PREFIX
before (in time, place, order, degree, or importance)

So there is much overlap in the meaning. I would say the difference is that pre- is much more common. You would say "in pre-Covid times". Do not say "in ante-Covid times" unless you are an expert speaker of English and know what you are doing.

• pro (w/abl) > position and separation (pro + ject = from a point --> departure)
• ante (w/acc) > location and direction (ante + chamber = before the room, --> towards it) whereas > (ante + mortem = before death <-- prior to it)
• prae (w/abl) > place where = position (pre + fer =put before --above all)

One may keep these in mind in understanding the basic difference–not always so clear, but gives the notion based on Latin.

It really does not matter if there is a distinction between pr[a]e and ante. The tendency is as follows:

The pre- prefix has entered English directly from Latin, and French and has been used to create words in English from Late Middle English onwards chiefly with the added meaning of "before [with respect to time] prenatal - before [the time of] the birth.

The ante- prefix has has entered English directly from Latin, and French and has been used to create words in English from the 17th century onwards chiefly with the added meaning of "before [with respect to space or time]", e.g. antenatal before [the time of] the birth / antechamber before (place) the main chamber.

Origins and eytomology from OED:

English anteroom adj. Origin: A borrowing from Latin, combined with English elements. Etymons: ante- prefix, Old English hrum (rare).

Latin - Antecede: antecēdere antecede v Origin: A borrowing from Latin. Etymon: Latin antecēdere.

1628 T. Spencer Art of Logick 239 This Axiome..containes nothing that doth antecede, or follow.

antestomach n.

French: Etymology: < Old French estomac, stomaque, stomeque (modern French estomac)

1678 J. Ray tr. F. Willughby Ornithol. i. 17 The Gullet..in many birds of this kind immediately above the stomach is dilated into a kind of bag or ante-stomach.

Pre- :

Latin: prae-ambulāre to walk before (see preamble)

French: preeminence, Etymology: < Middle French preeminence, preeminance, preheminance, prehemynence.

English: predestiny Etymology: < pre- prefix + destiny n. Etymology (destiny): Middle English,