Ansbach to Nuremberg

S stands for S-Bahn, a commuter train. It does take a little longer because it make frequent stops. It doesn't have coach-type seating; the seats are designed for people getting on and off quickly. IC, of course, stands for InterCity, a fast train, and travel by IC will cost more than regional train travel. RE stands for regional express, a regional train, but an express in that it does not stop at every station. You can use both the RE and the S-Bahn with a Bayern-Ticket. You can see the price of the IC ticket on the Bahn website. The Bahn website doesn't show the price of the RE and S-Bahn because they don't sell the tickets online. That trip is in a traffic district (Verkehrsverbund), Verkehrsverbund Großraum Nürnberg. You can find the price of a local ticket (9,10€, one way) on the VGN website.

Thanks again Lee for your help on the German train system! Are there lockers for carry on bags in Ansbach,Wurzburg and Nuremberg?

I think they probably all have locker, particularly Würzburg and Nürnberg. I'll check. After checking the Stationsdatenbank on the Bayerische Eisenbahngesellschaft website: Ansbach does, on the passageway leading from the station building to the tracks. Looks like in Würzburg they are on the outside of the station building, on the track side. In Nürnberg, they seem to be at either end of the West tunnel. I seem to remember there being lockers just off the East passageway when I was there in 2007, but I don't see them on the map. The station layout on the Bahn website https://cms-bahnhof.noncd-web.db.de/sites/default/files/pdf/nuernbergplandb_vst_a4web_0.pdf shows them at the far end of the west tunnel and in the basement to the west of the main entrance. If you are doing more than just Ansbach to Nürnberg, you might want to get an entire network Tagesticket (day pass) for 16,80€.