Minister and priest are both terms used in the Anglican Church. Minister is the broader term and has a basic meaning (whether as verb or noun) of “to render aid or service”. In a church context the word “minister”, used as a noun, refers to a clergyperson. In the Anglican Communion, generally speaking, anyone who has been ordained to one of the three orders of deacon, priest or bishop is a “minister” although it is most commonly used to refer to one who is a priest (or “presbyter”).
Historically, Anglican prayer books of the sixteenth and seventeenth centuries retained the use of the word “priest” when speaking of ordination i.e. “The form and making and consecrating of Bishops, Priests and Deacons” (spelling modernized). In the body of the Prayer Books of 1549 and 1662 the term “minister” is generally used in the rubrics e.g. in the Introduction to The Lord’s Supper or Holy Communion: “If a Minister be persuaded that any person who presents himself to be a partaker of the holy Communion”; or in the body of the text when it denotes who shall make what response, the terms “Minister” and “People” are used. In other rubrics, e.g. in the service of Morning Prayer, the term priest is used, i.e.: “The Absolution or Remission of sins is to be pronounced by the Priest alone, standing: the people kneeling”.
The use of the term “priest” was, however, much less common in general or ecclesiastical usage before the mid-nineteenth and early twentieth centuries. It tended to become part of the general division in the church between “Protestant” or “Low Church” and “Anglo-Catholic” or “High Church”. “Minister” was a term favoured by the Protestant/Low Church movement and “priest” (along with “Father” as a form of address) by the Anglo-Catholic/High Church movement.
Today, “priest” and “minister” are generally interchangeable with “priest” or “celebrant” most commonly used in liturgical texts. Other terms such as “pastor” are also widely used to describe those in an ordained leadership role especially in an ecumenical context.
Finally, as Colin Buchanan rightly notes in his definition of the term “Minister”:”The breadth of the word has been expanded in the 20th century to include ‘lay ministers,’ that is, people who are of the laity, but hold some kind of charter or authorization for tasks they fulfil. Its exact meaning therefore has to be determined by its context”. 
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 See Colin Buchanan, Historical Dictionary of Anglicanism. Lanham MD: The Scarecrow Press. 2006, vide “Minister”.