oneway & return ticket
the price for a return ticket is almost always the same as two single tickets, there is however a difference if you need a refund.
Anytime tickets (Normalpreis, either with Bahncard-discount or not) can be refunded free of charge up to one day before the first day of validity and a fee of 17,50 thereafter.
Advancetickets can be refunded for a fee of 17,50 up to one day before departure only.
Cancelling an advance return ticket will cost the 17,50 fee only once while two separate oneways add up to a 35,00 fee. On the other hand you can not get a refund for the inbound portion of a return ticket after the outbound has been used.
In theory there are three categories of trains on the national rail network in Germany:
local fares (Nahverkehr) is the cheapest and only valid on slow trains, although you can upgrade anytime local to a faster train ticket with a supplement called productchange (Produktwechsel). Upgrades are not availible for heavily discounted tickets, especially the Schönes Wochenende, Quer-durchs-Land or Ländertickets, which offer unlimited travel on local trains, or student tickets.
Intercity (including Eurocity) fares are slightly more expensive than local fares and allow travel on the mainline, but not on high speed trains. They are also valid on local trains, though you will not get a refund if you travel on a slower service.
ICE (Intercity Express) fares are valid on the highspeed trains, essentially the ICE, but also the austrian Railjet and the domestic part of the TGV to France. They too are valid on slower trains.
Most areas in germany are also part of a regional fare scheme which usually uses either zones or townborders for their farestructure. Within these areas the same ticket is valid for local trains, tramways and busses, but there is usually no bahncard-discount and the "normal" local fares from DB are not availible for journeys within one regional network (but again for travel between different networks)
The Thalys trains from Essen to Aachen via Duisburg, Dusseldorf and Cologne (and on to Brussels and Paris) is a complete alien and can not be used with any Deutsche Bahn tickets. Thalys tickets are also no longer sold at german railwaystations, the only option is to book online or buy a very expensive ticket on board.
Advance tickets are availibe while stocks last and up to one day prior to departure. They can be combined with a Bahncard25 discount, but not with Bahncard50. The availibility of advance tickets relies on the mainline trains only, so you can sometimes get a massive discount if you travel certain parts in local trains if there is no advance fare availible for that segment, though this involves considerable amounts of guesswork and hit and miss. It is compulsory to use the main line trains indicated on the ticket, but except in first class there is no seat reservation included. When the tickets includes one or several portions on local trains you can choose any local train that suits you, but not upgrade to mainline trains.
Some special fares are not sold by Deutsche Bahn directly but through other websites, notably comparison sites for long distance coaches or the german lastminute website ltur.com. These tickets can be considerably cheaper than normal advance tickets, but the can not be cancelled or changed at all, are only availible online and are valid for selected routes on mainline trains only. There is also no discount for bahncard holders.
Onlinetickets are valid for the person whos name is indicated on the ticket and must be combined with a certain form of identification. Most credit- and bankcards will do, any Bahncard or the free bahnbonus-card or german passports or id-cards. Paper tickets from ticketmachines or railway station bear no name and can be used by anyone else.
It is well worth to apply for a free bahnbonus-card, they are valid as ID for onlinetickets and you usually get 500 free points for signup, which is already sufficient for some rewards. There are infrequent but numerous special offers where you either get a reduced price for certain destinations or plenty of free points if you travel within a certain period.
Both bahncards (those with a discount) and bahnbonuscards also allow to collect status points towards the elite level bahncomfort, which essentially gives lounge access at large stations, though the status itself can only be used if you own a bahncard.
eCoupons are discount codes which are distributed either via newsletter or facebook or sometimes promotional leaflets or on certain products in supermarkets. They can only be used once and are (in theory) not transferable. Another frequent special offer is a free companion ticket (Mitfahrerfreifahrt), though these are oneway only and the return has to be paid unless you have a second companion ticket.
There are some other companies operating certain francises on the national rail network, but they usually use DB fares and ticketing. HKX, a private train from Cologne to Hamburg, sells its own tickets but nowadays also accepts DB tickets, with the exception of certain local fare tickets. Some traincompanys accept tickets with bahncard discount, but do not sell those tickets on their own ticketmachines, in this case the adjacent machine from Deutsche Bahn offers better value.
Free travel for students is usually valid for busses, trams and local trains in the area, though one has to read the smallprint carefully.
Split tickets can sometimes be cheaper than a through fare, but you loose the right for alternative travel if you miss your connection. If you miss a connecting train during a journey that is covered by the same tickets DB has to get you to your final destination somehow (that might include alternative trains, a taxi or hotel) and pay a compensation for the delay. If you travel on two separate tickets it is your quest to reach the second part in time so allow plenty of connecting time- you may get a refund for the delay of the first part, but the second ticket is void.