Timothy and Titus through the laying on of hands became the successors of the Apostles which became known ultimately as Bishops and performed the same functions as the Apostles.
The apostles thus set up first the office of deacon, then priest, then bishop. Every organization that grows tends to reallocate its functions in this "bottom up" manner, reallocating of its most important functions last of all. There was an additional reason why the early Church did so: In the first generation of Christians, it took time for everyone to mature in the faith to the point that some could serve in office (1 Tim. 3:6). By late in the first century, it became clear that Christ did not plan to appoint new apostles to fill the roles of the originals. They had served a special purpose as the first link between Christ and all later Christians, but their office was temporary. They passed from the scene, leaving the three-fold structure of bishops, priests, and deacons in place.
In this early period, the names for the different offices were in flux. There was not yet an established terminology. Titles with secular origins were used. Diakonos (deacon) meant "minister" in Greek, presbuteros ("presbyter") meant "elder," and episkopos ("bishop") meant "overseer." Because all the offices involved ministering to others and overseeing certain things, the terms could be applied in different ways.
Thus Paul, an apostle, occasionally described himself as a diakonos (2 Cor. 3:6, 6:4, 11:23, Eph. 3:7), meaning simply a minister. Likewise Peter, also an apostle, once described himself as a fellow presbuteros (1 Pet. 5:1), meaning an elder figure of the Christian community. Presbyters could be described as episkopoi (Phil. 1:1, 1 Tim. 3:1-2, Titus 1:7), since they had the task of overseeing individual congregations, while those we now call bishops were termed "evangelists" (2 Tim. 4:5) because of their church-planting function.
By the end of the first century, the terms had acquired the fixed, technical meanings they have today. "Deacon" became the fixed description of the lowest order, "presbyter" (which was shortened to "priest") was the term for those who oversaw individual congregations, and "bishop" became the term for those who oversaw multiple congregations.