How are Lutheran weekday “prayer services” different from “matins” or “vespers”? From Wikipedia, matins:


  Lutherans preserve recognizably traditional matins distinct from
  morning prayer, but "matins" is sometimes used in other Protestant
  denominations to describe any morning service.


Assuming that the claim is true, what makes "morning prayer service" in the Lutheran church distinctly different from the matins? Perhaps, the matins has a particular structured order and is a specific form of the "morning prayer service"?
Matins and Vespers are prayer services prescribed for the morning and evening respectively, and the terms generally refer to services with particular orders of worship laid down in various hymnals used by the Lutheran denominations.  However, while "matins" is an order of worship established for use in the morning, there are some congregations, and some times, when a morning prayer service might not use the order prescribed for worship, and other times when the service might, indeed, use that formulary, but for some reason might choose the name "morning prayer" rather than "matins". 

In a Lutheran Church, I would expect a morning prayer service, though, would normally, though not exclusively use the order for matins.