Both in Luke and Acts the same Greek word is used
652 apostolos {ap-os’-tol-os} from 649; TDNT - 1:407,67; n m 1) a delegate, messenger, one sent forth with orders 1a) specifically applied to the twelve apostles of Christ 1b) in a broader sense applied to other eminent Christian teachers 1b1) of Barnabas 1b2) of Timothy and Silvanus
Interestingly, the English word apostle according to Webster Middle English, from Anglo-French & Old English; Anglo-French apostle & Old English apostol, both from Late Latin apostolus, from Greek apostolos, from apostellein to send away, from apo- + stellein to send
First Known Use: before 12th century
At any rate both of these, say that apostle means one who is sent not witness.
Two were put forward to replace Judas. Matthias and Joseph called Barsabbas were chosen like you said because they had accompanied the others from the time that the Lord Jesus went in and went out among us beginning with the Baptism of John to the resurrection. The way it is stated there were more than two but that these were the two put forward and the lot fell on Matthias who then was numbered among the Apostles that is one who is sent forth with orders.