Various churches have different ways of doing/implementing.
In the OPC, "evangelist" is viewed as a
function, a specially empowered (by the Presbytery) function of the ordinary ministerial office.
The office of Minister in our church encompasses the regular pastorate, the Teacher, and the Evangelist.
Most of us are called to a congregation and pulpit ministry, although some churches call pastors to other specified roles, such as private counselor, age-related service, or the like.
Teacher is a designation for ordained service in a church, seminary, college, or other setting which the call excludes most of the regular functions of the office, other than theological instruction.
Evangelist is a designation for someone in our church--a "missionary" (which is a more elastic term we also apply to the wife of an ordained man)--appointed to extend the church of Christ to a place that needs a church. We do not believe in the work of evangelism that does not include "organization" of those evangelized into a church (if not incorporated into an existing church).
Because an Evangelist typically works in a place where, by definition, there is no prior church-institute, he needs some unique authorization (in Presbyterian opinion). He needs permission/delegation of the power of the whole church to do alone (by himself) what is under ordinary, organized conditions the duty of the whole church together. It is an act of general consent--symbolized by the laying on of hands by all the Presbytery (1Tim.4:14)--that elders and ministers are ordained.
To put it in perspective ask the question: what right (that other men should inherently recognize) does a self-appointed man have to instantiate a church? Such an unaccountable man is perfectly aligned with the pope, with a bishop (in the hierarchical sense). He thinks he's an apostle. But, when we send out a missionary, we may perhaps be asking one man to do something that looks very much like what I just described pejoratively.
There is a difference, however. The evangelist is under authorization and entrusted with the power of the whole to extend the whole. He is a man under authority, accountable to his brethren. He is acting self-consciously for the many, and is no hierarchical bishop. He is not ordaining subordinates, but raising peers (in a sense); and he's doing so with the full approbation of all them who commissioned him. What he does in their name, they are prepared to acknowledge. So that, what is organized is not one whit less the church than the church that sought the new organization.
The key, according to this understanding of the function of the Evangelist, is that we do not simply "make disciples" or mere "followers-of-Jesus," and run off to a new place of endeavor, with no concern for the ongoing care of the sheep. Nor do we endorse the idea that now the sheep should find a fold for themselves. Neither can we in good conscience join up with the kind of modern "evangelistic crusade," where various "supporting churches" divvy up the follow up on decisions brought about by the traveling charismatic "evangelist."
Joining a convert to the visible church is part-and-parcel of the work of the Evangelist.
And that's my

worth.