First Rights, fnasr

[foxtale]

OK as best as I can understand, First Rights or one time rights means the purchaser has the first right to publish by a specific date. The author retains their copyright but is committed to not letting another publication of the work occur until the purchaser has published. (This may mean closing down the work if it is currently appearing in a website elsewhere.) Likewise fnasr is First North American Serial Rights, which gives the publisher first right to publish by a certain date, and also the right to publish the piece in a subsequent work such as their website or an anthology.
Does this jibe with your understanding?