Distinguishing an anti-piracy escort from a privateer

Would a private military company's craft protecting ships from pirates count as a privateer?

An escort or commissioned vessel of marque is the tentative classification offered if it does not capture enemy trade.

A commissioned vessel of marque or escort is the tentative classification offered for the hypothetical craft. The distinction made here turns on protecting ships from pirates rather than capturing enemy trade. No particular legal system or commissioning arrangement is examined.