Spar comes from the German verb "sparen, to save" and, when used as an adjective, means savings, as in SparPreis, savings price.

There are a number of savings fares available from German Rail, notably SparPreis and Dauer-Spezial. Both are limited in quantity and require at least a 3 day advance purchase. In addition they are for a specific day and train(s) and are non-transferable. In some cases, they can be partially refunded before the date of travel. Part of the trip has to be by express train (IC/EC/ICE).

The SparPreis 50 fare is round trip and requires a Saturday night stay. Because it is a 50% savings, a round trip costs the same as a full fare one way trip, but co-travelers (Mitfahrer) pay half of that, so, for two people, a round trip SparPreis fare, with the return ticket not used, is still less then full fare.

The Dauer-Spezial fare is a "tiered" fare. with limited quantity at each level. When the cheapest fares sell out, the next fares are more.

You should be able to find these under "Special fare" when you look for schedules and fares on http://reiseauskunft.bahn.de/bin/query.exe/en.

For shorter distances, there are the Schönes-Wochenende- and Länder-Tickets. With the €35 Schönes-Wochenende-Ticket, both of you can travel all day Sat or Sun, on any regional trains (RB, RE, IRE, and S-Bahn) anywhere across Germany, even across state (Länder) borders. With Länder-Tickets (e.g., Bayern-Ticket, €27), you can travel anywhere on regional trains in one Land for an entire day (after 9 AM weekdays).

For your trip from FRA to Bacharach, the most economical way is by regional train, full fare. There are two stations in the Frankfurt airport. The Regionalbahnhof is closer, under the building across the street from Terminal 1. You get to it by going down stairs just inside the streetside wall of the terminal. The local transit district (RMV) sells single trip tickets to Bacharach for €9,70 pP. Take any regional train or the S-Bahn (S8) to Mainz, then change there for Bacharach. Most regional trains leave the Mainz station for Bacharach on Gleis (track) 11. While most tracks go completely through the station, track 11 deadends in the station. It is adjacent to track 1, on the end opposite to where you come in from FRA.

HI DM
>I didn't see the SPAR fare. I did see the savings fare 25 50 but that requires round trip travel.

If the usual fare is more than 51E, buy the RT fare and don;t use the return ticket.

If you stay in Bacharach, the one way fare to Moselkern is €12,80 pP. That's about €51 for two, round trip!

However the local transit district (VRM) that includes both St. Goar and Moselkern charges €20 for a Preisstufe 10 (price level 10) Minigruppenkarte that would include both of you round trip from St. Goar to Moselkern and back.

From Bacharach, take the first ship (10:15) in the morning to St. Goar (10:55). After getting off the ship in St. Goar, walk up to the Bahnhof and purchase a Minigruppenkarte to Moselkern from the ticket automat (the station has no ticket counter) as well as two DB tickets to Bacharach at €3 each (you'll need those on your way back). Get on the first train (11:32) to Koblenz (12:03) and change there (12:31) to Moselkern (13:03).

On the return trip, the Minigruppenkarte covers you to St. Goar; the DB tickets cover your trip from there back to Bacharach.

In St. Goar you will have almost 40 minutes to walk up the hill, find the Bahnhof (behind the church), and figure out the ticket machine. Buy the Minigruppenkarte first. Then if you don't have time to get the Bahn tickets back to Bacharach, you can get them in Koblenz.

Alternatively, if you prare going to stop for lunch somewhere, buy your tickets first, then walk down the hill and find a restaurant. Take the 12:32 train to Koblenz and Moselkern.

For your trip from Bacharach to Berlin, I assume that's May 30. I found Dauer-Spezial fares on several connections for €129 for two people using an ICE. I also found €109 for two for a slightly slower connection leaving Bacharach at 8:26 and using an IC.

If you want this price, you need to get your tickets soon!

Although the OP referenced Bacharach in her first post, it looks like she has booked a hotel in Boppard instead. She also mentioned that she might be interested in spending a little time in Cologne en route to Berlin.
The best rate currently from Boppard to Berlin on 30 May is 109 Euros total for both passengers. However, for 45 euros total for both passengers, OP can take the 9:50 train from Boppard to Cologne, arriving at 11:05. They can then spend the day in Cologne and catch the 18:49 ICE train to Berlin for 49 Euros total for both (This is a Dauer-Spezial rate). Don't wait long to purchase this ticket. Use the link provided by Larryincolorado.
Assuming a travel date of 4 June from Berlin to Munich, there is currently a special rate of 49 Euros total for both passengers, departing at 13:00 and arriving at 18:40. Also don't delay in purchasing this special fare ticket.