Yep, it is enlightening.
In John, Jesus is the paschal lamb that is sacrificed on Passover. That is why the timing of the crucifixion is different in John compared to the synoptics so Jesus could be sacrificed at the right time -- thus John 19:14, 31 places the crucifixion on Preparation Day at about the time the lambs are slaughtered. The word used for lamb in John 1:29, 36, namely amnos, also reflects an exegetical tradition on the Suffering Servant of Isaiah 53:7-8 LXX (which has been merged with the paschal imagery), a tradition which is also independently attested (indeed, overtly quoted) in Acts 8:32-33 and 1 Peter 1:19 which is also sacrificial, if not paschal, in alluding to the "precious blood of a spotless and stainless lamb (amnos)" that has paid the ransom. Each usage of amnos is thus steeped in this symbolism, and the same applies to other early Christian writings, such as 1 Clement 16:7 ("like a lamb [amnos] before his shearer is dumb so he did not open his mouth") and Barnabas 5:2.
The other word, arnios, instead has a strong pastoral sense. The sense in Greek is that arnios is more of a pet lamb that one cares for, protects, and loves -- not offers up in sacrifice. The sense of protecting lambs also implies their vulnerability in the face of danger. Thus the pastoral duty of Peter in John 21:15 involves caring for the lambs (disciples) of Jesus. A key text is that of Luke 10:3 wherein Jesus says "I send you out as lambs (arnas, plural) in the midst of wolves". Again, the disciples are the lambs and they face danger from "wolves". The usage of arnios in Revelation is also similar. In Revelation 7:17, the Lamb is "to be their shepherd; he will lead them to the springs of living water", and the disciples in 14:4 "follow the Lamb wherever he goes". There is also the image of the Lamb in the face of dangerous wild Beasts, who in 17:4 "make war against the Lamb." On the other hand, there is also an element of the Johannine concept relating "lambhood" to Jesus' death; thus in 5:6 the Lamb "looked as if he had been slain" (cf. v. 12), and 12:11 refers to the "blood of the Lamb". However, these two statements are not overtly paschal as the statements in 1 Peter, Barnabas, etc. and the conception of Jesus in John. I would say that the concept of arnios here draws on both pastoral and paschal imagery, while the pastoral sense is missing in the case of amnos.