The two words are used as metaphors. Lambs, ἀρνία, actually "little" lambs means the Jewish people who have not yet believed or have rejected, Jesus as the Christ. Sheep, πρόβατά, is used as a metaphor for the Jewish people who do believe and accept Jesus as the Christ.
15 When they had finished breakfast, Jesus said to Simon Peter, “Simon, son of John, do you love me more than these?” He said to him, “Yes, Lord; you know that I love you.” He said to him, “Feed my lambs.” (βόσκε τὰ ἀρνία μου) 16 He said to him a second time, “Simon, son of John, do you love me?” He said to him, “Yes, Lord; you know that I love you.” He said to him, “Tend my sheep.” (ποίμαινε τὰ πρόβατά μου) 17 He said to him the third time, “Simon, son of John, do you love me?” Peter was grieved because he said to him the third time, “Do you love me?” and he said to him, “Lord, you know everything; you know that I love you.” Jesus said to him, “Feed my sheep." (βόσκε τὰ πρόβατά μου) (John 21) [ESV]
The passage can be considered by sequence of instructions, by the type of action to be taken, or by type of animal used (metaphorically):
- First: Feed/lambs βόσκε τὰ ἀρνία μου "feed the lambs of me"
- Second: Tend/sheep ποίμαινε τὰ πρόβατά μου "tend the sheep of me"
- Third: Feed/sheep βόσκε τὰ πρόβατά μου "feed the sheep of me"
- βόσκε (feed): my lambs (ἀρνία) and my sheep (πρόβατά)
- ποίμαινε (tend): my sheep (πρόβατά)
- ἀρνία (lambs): feed (βόσκε)
- πρόβατά (sheep): tend (ποίμαινε) and feed (βόσκε)
The first action, "feed" is βόσκε and means to feed or to graze. The second action, "tend" is ποίμαινε (from the root ποιμήν meaning shepherd) and means either to feed, to tend a flock or to rule or govern. The arrangement of the three actions makes sense. First the animals are feed. Then they are tended to, and then they are feed again. In this case, the instructions about the sheep (tend and feed) imply they have already been fed.
While it is logical to see a progression of lambs to sheep, this is not quite consistent with the etymology of ἀρνίον (lamb) which is the diminutive of ἀρήν. Etymologically, one expects a ἀρνίον to become a ἀρήν before being considered to be a ποίμαινε:
ἀρνίον --------> [ἀρήν] ---> ποίμαινε
little lamb ---> lamb -----> sheep
If a relationship between ἀρνίον and ποίμαινε is intended, one must consider ἀρήν has been purposely omitted from the passage. In other words, since the essence of the message is unchanged regardless of which lamb was fed, the choice to use ἀρνίον instead of ἀρήν should be considered purposeful. Two conclusions can be drawn:
- ἀρνίον was used to give emphasis to "little" lambs 1
- ἀρνίον was used to avoid caking them ἀρήν
ἀρήν is used once in the New Testament:
Go your way; behold, I am sending you out as lambs in the midst of wolves. (Luke 10:3)
The 72 (disciples) were sent as ἀρήν. If we assume they had been ἀρνίον, that is, diminutive ἀρήν, before becoming disciples, then the metaphoric progression of these specific disciples was:
- ἀρνίον - Jewish people in general
- ἀρήν - Jewish disciples of Jesus, before the Crucifixion and Resurrection
- ποίμαινε - Jewish believers in Jesus as the Christ after the Crucifixion and Resurrection
If this is so, then the three instructions to Peter become:
- Feed (that is, evangelize) My little lambs, the Jewish people who rejected Me
- Tend (that is, shepherd) My sheep, the Jewish people who believe in Jesus
- Feed (that is, encourage) My sheep, the Jewish people who believe in Jesus
From the context, Peter's primary mission is to the Jewish people. He is to preach the Gospel to those who rejected Jesus and tend to and feed (shepherd and encourage) those who do believe.
Essentially, Jesus is rebuking Peter for how he is shepherding the sheep. Instead of preaching the Gospel and encouraging the disciples to be fishers of men (Matthew 4:19, Mark 1:17, Luke 5:10). Peter has gone back to his days as a fisherman (John 21:4). His decision has led six other disciples to follow him. So Jesus tells Peter to get back to work. Preach the Gospel to those Jewish people who heard but do not believe and shepherd and encourage those who do believe.
1. The diminutive could mean size, or age, or simply "lesser." For example, a lamb not chosen to be sacrificed could reasonably be called a ἀρνίον relative to the lamb, ἀρήν, which was chosen, despite being the same age and size.