In the NT the term “apostle” is used in three different ways.
First, there are the Twelve that Jesus named “apostles” (Matt 10:2–4 = Mark 3:16–19 = Luke 6:13–16; Acts 1:13). This seems to refer to the office of the apostle. Acts 1:21–22 indicates that to qualify as an apostle one must have been with the Lord in his earthly ministry and must have witnessed his resurrection body (Acts 1:21–22; 4:33; 2 Pet 1:16; 1 John 1:1). The witness of the Twelve to Christ’s resurrection is affirmed by Paul (1 Cor 15:5).
Second, there were apostles in addition to the Twelve. There were Barnabas (Acts 14:4, 14; 1 Cor 9:5–7), James, the Lord’s brother (1 Cor 15:7; Gal 1:19), and Apollos (1 Cor 4:6, 9), probably Silvanus (1 Thess 1:1; 2:6 [GT 2:7]), Titus (2 Cor 8:23), Epaphroditus (Phil 2:25), and possibly Andronicus and Junia(s) (Rom 16:7). Paul mentions James and all the apostles (1 Cor 15:7) as distinct from Peter and the Twelve (15:5). In Gal 1:18–19 Paul states that when he went up to Jerusalem he visited Peter and he did not visit other apostles except James, the Lord’s brother. Hence, Paul recognized apostles beyond the Twelve. These are most likely those who were endowed with the gift of apostleship because they did not meet the above mentioned qualifications for the office.
Third, there was Paul who was an apostle (1 Cor 9:1; 15:9) and yet had not been with Jesus in his earthly ministry but did, however, see the Lord in his resurrection body. Hence, he claimed that he was born out of due season (1 Cor 15:8). Rather than trying to include him in either of the two categories above, it is best to see Paul as an exception to the rule and make a third category. It seems that he had the office of an apostle for the following reasons: (1) he used authority as an apostle (1 Cor 4:9; 9:1, 5; 11:5; 12:11–12); (2) he performed miracles (Acts 13:8–11; 14:3; 19:11; 2 Cor 12:12) that seemed to be done by those who had the office (Acts 2:43; 5:15–16; Heb 2:4); (3) his laying on of hands brought the Holy Spirit to the believers (Acts 19:6) such as happened to Peter (Acts 8:17); and (4) his greetings in most all of his letters (see passages above) are similar to those of Peter (1 Pet 1:1; 2 Pet 1:1). It would not be likely that he would have referred to himself as an apostle in his formal greetings if he had only the gift. Thus, this third category is an exception exclusive to Paul.
Hoehner, H. W. (2002). Ephesians: An Exegetical Commentary (pp. 134–135). Grand Rapids, MI: Baker Academic. Emphasis and paragraphing mine.