Rail Europe website versus DB

Understand that Rail Europe is a travel agency selling tickets to North Americans. It is NOT a railroad company. They do not sell all tickets for all routes. DBahn is the national railroad of Germany. They sell only tickets for trains starting or ending in Germany. I would purchase only from DBahn.

You will almost certainly pay more if you use RailEurope, which has a service charge and may not be using a terribly current/favorable exchange rate. At the least I'd price out each trip on the Deutsche Bahn website so I'd know the price-penalty for using RailEurope instead. And it is true that you won't necessarily see all the options on RailEurope.

Seconded. First choice for buying tickets should be the rail company actually running the trains, not a reseller in a different continent.

DB = Deutsche Bahn = German Railways = https://www.bahn.com/en/view/index.shtml

For other countries it would be different companies.

Also be aware DB sells a number of local special offers. Notably the "Länder tickets", valid in for unlimited travel (train + bus) in one "Land" (German state) for one day. These are sold for 1-5 passengers, and are extra value the more people who ravel together.
You do not need to buy these in advance, there is no discount for doing so. You just buy them from a station ticket machine.

Info here: https://www.bahn.com/en/view/offers/regional/regional-day-tickets.shtml

What specific journeys are you planning to take? There are trips within Germany you might take which are not sold by DB at all, but by the local transport authorities. It would be good for us to look at your list of journeys so as to advise you where to buy those non-DB tickets (if any.) You might get other helpful tips on DB ticketing as well. I recently traveled from Düsseldorf to Budapest with a 2-night stopover near Salzburg for a total of €50.

DB has recently expanded it's online sales options to including almost any train touching Austria, as well as almost any train touching Germany, which is a lot! But you put this on the German page, so maybe Germany is all you need. Since the DB site is as easy to use as any in Europe, you probably don't need the built-for-Americans features of Rail Europe, but the option is there in case you do.

Just choose the "English" button on any of the national rail websites...they're built for "Americans", too.

Thanks to everyone for your advice. The two train trips I am researching are: (1) Rothenberg ob der Tauber to Cologne and (2) Freiburg, Germany to Geneva, Switzerland. I don't think the Länder tickets will apply here, but it sounds like DB is the way to go. Many thanks!

Then forget Rail Europe.

For any train in Europe, your first place to try to buy tickets should be the company operating the train. You would only use another website if there was a problem buying the tickets. For instance, some sites do not work with US credit cards.

DB's site is very easy to use and takes US credit cards just fine (at least it did a few years ago when I last used it), so there's no need, and no advantage, to buying from anyone else.

Here's a great list of where to buy tickets for European trains, from rail guru The Man In Seat 61: https://www.seat61.com/Europe-train-tickets.htm

There are trips within Germany you might take which are not sold by DB at all, but by the local transport authorities.

Case in point would be Frankfurt airport (FRA) to Bacharach. The Bahn won't sell you a ticket online, because these tickets are sold by the Frankfurt metro district, RMV (Rhein-Main-Verkehrsverbund, www.rmv.de). RMV sells a ticket from FRA to Bacharach for €12,50 pP ($13.57). RailEurope sells the same ticket for $25, even without their "Services fee".

You can buy RMV (and most other Verbund-) tickets via the DB app.

Thanks to everyone for your advice. The two train trips I am researching are:
(1) Rothenberg ob der Tauber to Cologne, and
(2) Freiburg, Germany to Geneva, Switzerland.
I don't think the Länder tickets will apply here

No, I don't think so, Länder ticket are specific to Germany, but for Freiburg to Geneva, you should be able to find tickets, even SparPreis tickets, on the Bahn website. Unlike for other countries, the Bahn sells tickets with connections in Switzerland.

And, for long trips, like Rothenburg to Köln, you probably don't want to use regional trains, which a required for using a Länder ticket. For long distance trains, like ICE, IC, and EC, you can get good prices by purchasing in advance with SparPreis.