"Master" and Lord
In their prayer the disciples use different terms when addressing God and referring to Jesus:
23 After their release, Peter and John returned to the brothers and sisters and reported everything the chief priests and elders had said. 24 They listened, then lifted their voices in unison to God, “Master (δέσποτα), you are the one who created the heaven, the earth, the sea, and everything in them. 25 You are the one who spoke by the Holy Spirit through our ancestor David, your servant: Why did the Gentiles rage,
and the peoples plot in vain?
26 The kings of the earth took their stand
and the rulers gathered together as one
against the Lord (κυρίου) and against his Christ. 27 Indeed, both Herod and Pontius Pilate, with Gentiles and Israelites, did gather in this city against your holy servant (παῖδά) Jesus, whom you anointed. 28 They did what your power and plan had already determined would happen. 29 Now, Lord (κύριε), take note of their threats and enable your servants to speak your word with complete confidence. 30 Stretch out your hand to bring healing and enable signs and wonders to be performed through the name of Jesus, your holy servant (παῖδά).” 31 After they prayed, the place where they were gathered was shaken. They were all filled with the Holy Spirit and began speaking God’s word with confidence.
(Acts 4 CEB)
Translations like the CEB render δεσπότης as "Master" to properly distinguish how the disciples address God and Jesus, κύριος ("Lord," the word Paul uses).
The term παῖς means either son or servant. Calling Jesus the "παῖς" (verses 27, 30) is an expression of Christ as the Suffering Servant described in Isaiah:
And he said to me, “It is a great thing for you to be called my servant (παῗδά) so that you may set up the tribes of Iakob and turn back the dispersion of Israel. See, I have made you a light of nations, that you may be for salvation to the end of the earth.”
(LXX-Isaiah 49:6 NETS)
See my servant (παῗς) shall understand and he shall be exalted and glorified exceedingly. (LXX-52:13 NETS)
The title of Pais best describes the earthly work of Jesus: He is the Anointed Servant who suffers on behalf of others because God has placed others sin on Him.
1In particular, the disciple's prayer seems to draw from this Suffering Servant passage:
Who among you is the one who fears the Lord? Let him hear the voice of his servant (παιδὸς). Those who walk in darkness – they have no light; trust in the name of the Lord, and lean upon God. (LXX-Isaiah 50:10 NETS)
Since παῖς means "son" or "servant" both refer to Jesus: He is the Servant-Son Isaiah predicted would come. On the use of παῖς to describe Jesus Oscar Cullmann says:
These passage openly give Jesus the actual title of παῖς τοῦ Θεοῦ, the Septuagint's translation of Deutero-Isaiah's expression of ebed Yahweh. We find this title four times in Acts. It is significant that all four occur in the same section, chapters 3 and 4, and that Jesus is designated παῖς τοῦ Θεοῦ in no other book of the New Testament. Jesus is called this first in Acts 3:13, which refers to Isaiah 52:13; then again in Acts 3:26, which actually deals with a Christological title: Jesus is called Pais exactly as he later is commonly called 'Christ.' One gains the clear impression also in the next chapter (4.27, 30) that παῖς is used almost as a terminus technicus which has a tendency to become a proper name - as did happen in the case of 'Christ.' This confirms the existence of a very old Christology on the basis of which Jesus was called the ebed Yahweh.
Paul does not use the term παῖς to refer to Jesus
3but "only the direct quotations are absent. In three of the most important Christological passages of the letters of Paul (1 Corinthians 15.3; Philippians 2.7; Romans 5.12 ff.), the idea of vicarious suffering of the Servant of God is undoubtedly present."
4Rather than Pais Paul uses Kyrios, Lord:
...since Paul can see Christ only in the light of the event of the resurrection, he must make use of another title to designate Christ's person and work - the title of Kyrios, which points to the exalted Lord who allows his Church to take part in the fruits of his atoning death and who at the same time continues his function as Mediator.
Both terms, "servant" or "Son" and "Lord" accurately describe the Christ. The difference is one of emphasis. One focuses on the earthly ministry which initiated the Church; the other on the Lord who is head of the Church.
Finally, if the title of Pais is used for Jesus, then disciples would be properly called παιδίον, the diminutive of pais (cf. John 21:5 also 1 John 2:13, 18). As such Jesus or the Holy Spirit could be called their "Master." In this case the difference would be similar to a young child under going training παιδίον under the direction of their Master and a more mature child serving their Lord.
There is consistency in these passages (and throughout the NT) on the use of "Lord" (κύριος, Kyrios) as the exclusive title for Jesus. Even the disciples in prayer preserved the distinction.
The term "Master" is not exclusive to either the Father or Jesus:
“Master, you are the one who created the heaven, the earth, the sea, and everything in them. (Acts 4:24)
yet for us there is one God, the Father, from whom are all things and for whom we exist, and one Lord, Jesus Christ, through whom are all things and through whom we exist.
(1 Corinthians 8:6 ESV)
Both passages understand the necessity for both to bring about creation; just as Peter and Paul understand the necessity of both to bring about salvation. One cannot speak of either creation or salvation without Christ.
1. Oscar Cullmann, The Christology of the New Testament, Revised Edition, translated by Shirley C. Guthrie and Charles A. M. Hall, The Westminister Press, 1963, p. 77
2. Ibid., p. 73
3. Likewise Peter (cf. 1 Peter 2:21) later makes reference to the Suffering Servant but uses "Christ." The shift could result from a later emphasis or reflect an audience which is no longer exclusively Jewish and might fail to understand the Old Testament significance of Pais.
4. Cullmann, p. 76
5. Ibid., pp. 77-78