Albert Barnes on John 21:16

Feed my sheep. The word here rendered feed, as has been remarked, is different from the word in the previous verse. It has the sense of governing, caring for, guiding, protecting --the kind of faithful vigilance which a shepherd uses to guide his flock, and to make provision against their wants and dangers. It may be implied here that the care needed for the young in the church is to instruct them, and for those in advanced years both to instruct and govern them.

My sheep. This term commonly denotes the church in general, without respect to age, John, chapter 10.

(k) "Feed my sheep" Heb 13:20, 1Pet 2:25