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The word "Apostle" iterally means "one who is sent". The Lord himself is called an apostle as one sent by his Father (Hebrews 3:1 and cf John 20:21). However, the word "apostle" is generally used of the body of disciples, called "the twelve", to whom our Lord entrusted the organization of his church and the preaching of his gospel (Matthew 10:1-5; Mark 3:14-16; 6:7; Luke 6:13,14; 9:1; Acts 1:13). Our Lord gave them the "keys of the kingdom," and by the gift of his Spirit enabled them to build the foundation of his church (John 14:16,17,26; 15:26,27; 16:7-15). Judas Iscariot, one of "the twelve," eliminated himself from the number of the twelve, and Matthias was substituted in his place (Acts 1:21). Saul of Tarsus was afterwards added to their number (Acts 9:3-20; 20:4; 26:15-18; 1 Timothy 1:12; 2:7; 2 Timothy 1:11).
Luke has given some account of Peter, John, and the two Jameses (Acts 12:2,17; 15:13; 21:18) but beyond this we know nothing from authentic history of the rest of the original twelve. After the martyrdom of James the Apostle (Acts 12:2) James the Less usually resided at Jerusalem, while Paul, "the apostle of the uncircumcision," usually travelled as a missionary among the Gentiles (Galatians 2:8).
The qualifications of an Apostle are listed as follows:
that they should have seen the Lord, and been able to testify of him and of his resurrection from personal knowledge (John 15:27; Acts 1:21,22; 1 Corinthians 9:1; Acts 22:14,15)
They must have been called to that office by Christ (Luke 6:13; Galatians 1:1)
It was essential that they should be inspired, and thus secured against all error and mistake in their public teaching, whether by word or by writing (John 14:26; 16:13; 1 Thessalonians 2:13)
Another qualification was the power of working miracles (Mark 16:20; Acts 2:43; 1 Corinthians 12:8-11)
Given these qualifications, the twelve Apostles could have had no successors.*
The bottom line is that a disciple is a follower but an apostle is one who was given a special commission and authority. In Jesus' day there were many disciples but only 12 apostles. All apostles are also disciples but only a few disciples [ i.e. 12 ] were apostles.
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* Note: The answer above was adapted from an article in Easton's Revised Bible Dictionary