Ars nova simply means "new style"; ars antiqua means "old style".
There are Wikipedia articles on ars nova and ars antiqua which explain a bit about the different styles and the composers associated with them.
Wikipedia pegs the development of the ars nova movement as being between the years 1310 and 1370 in France and the lowlands of the Netherlands.
In the section Ars Nova versus Ars Antiqua, the article describes the ars nova as being a rapid change in musical expressiveness. In this period secular music developed increased sophistication in polyphony and rhythmic complexity, in keeping with new conventions for music notation for expressing these concepts.
Ars antiqua, therefore, refers to any styles of music in use before the ars nova period began.
The terms prima prattica and secunda prattica, on the other hand, were terms used by Monteverdi around the year 1600, almost three hundred years later, so you are correct -- the terms and the musical styles represented have nothing at all to do with the terms ars nova and ars antiqua.