The word minister covers a wide and structurally varied set of Protestant clergy because it names a function, ordained leadership of preaching, sacrament, and pastoral care, rather than a single office defined the same way everywhere. In Presbyterian and Reformed polity a minister is a teaching elder, ordained by a presbytery and accountable to it alongside the local congregation's own governing session, reflecting that tradition's conviction that authority rests with a plurality of elders rather than any individual. Methodist polity historically ordains ministers into a connectional system in which a bishop or conference appoints ministers to specific churches for a set period, so an individual congregation typically has less say over who its minister will be than in more congregational traditions.
Congregationalist and many independent or nondenominational churches, by contrast, place the calling and ordaining authority almost entirely with the local congregation itself, which examines and calls its own minister with comparatively little denominational oversight. These structural differences mean two people both properly called minister within different Protestant traditions can hold quite different relationships to their denomination, their congregation, and the wider body of clergy around them, even though both preach, administer the sacraments, and provide pastoral care in broadly similar ways.