Disciple is mathaytes in Greek. It means learner, or student.
Apostle is apóstólos in Greek. It means one who is sent as a messenger or envoy. The Apostles were messengers.
And he went up on the mountain, and called to him those whom he desired; and they came to him. And he appointed twelve, to be with him, and to be sent out to preach and have authority to cast out demons: Simon whom he surnamed Peter; James the son of Zeb’edee and John the brother of James, whom he surnamed Bo-aner’ges, that is, sons of thunder; Andrew, and Philip, and Bartholomew, and Matthew, and Thomas, and James the son of Alphaeus, and Thaddaeus, and Simon the Cananaean, and Judas Iscariot, who betrayed him. (Mark 3:13-19)
And when it was day, he called his disciples, and chose from them twelve, whom he named apostles; Simon, whom he named Peter, and Andrew his brother, and James and John, and Philip, and Bartholomew, and Matthew, and Thomas, and James the son of Alphaeus, and Simon who was called the Zealot, and Judas the son of James, and Judas Iscariot, who became a traitor. (Luke 6:13-16)
Jesus commissioned these to perform that mission, go preach and teach and baptize just prior to his ascension to Heaven.
Now the eleven disciples went to Galilee, to the mountain to which Jesus had directed them. And when they saw him they worshiped him; but some doubted. And Jesus came and said to them, “All authority in heaven and on earth has been given to me. Go therefore and make disciples of all nations, baptizing them in the name of the Father and of the Son and of the Holy Spirit, teaching them to observe all that I have commanded you; and lo, I am with you always, to the close of the age.” (Matthew 28:16-20)
They received power to do this at Pentecost.
But you shall receive power when the Holy Spirit has come upon you; and you shall be my witnesses in Jerusalem and in all Judea and Sama’ria and to the end of the earth." And when he had said this, as they were looking on, he was lifted up, and a cloud took him out of their sight. (Acts 1:8-9)
Peter stood up and spoke out boldly after Pentecost. They received power to become witnesses. The word witness in greek is martyr. The Apostles are messengers, trained by Jesus, commissioned at his ascension and given power to do so at Pentecost.
-Tim-