The word minister was already ordinary English, meaning servant, before the Reformation put it to religious use, and its adoption reflected a deliberate rejection of priest as a title carrying sacrificial connotations the reformers wanted no part of. Calvin's Geneva and the Scottish Kirk that followed his model built minister into the standard title of the ordained clergy, and it travelled with Presbyterian, Congregationalist and later Methodist emigration to North America, Africa and Asia.
Usage has since spread well beyond the Reformed family in everyday speech. In British English especially, minister is used loosely for any Protestant or Nonconformist clergyperson, Baptist, Methodist, United Reformed or independent, regardless of that church's own formal polity, so the generic sense now sits alongside the precise Reformed sense of minister of word and sacrament ordained by a presbytery.
The office has followed the same broad Protestant pattern of expansion and contraction: declining stipendiary numbers in long-established Reformed churches in Europe, denominational splits over the ordination of women and of LGBTQ ministers within the last several decades, and continued growth of Presbyterian and Reformed church membership in parts of Africa, Korea and elsewhere, where the office is entered along the same lines of training and presbyterial ordination but exercised in a very different institutional setting.