In general, if a German city name has some qualifier like a river or geographic descriptor (e.g. Limburg a. d. Lahn, Kempten i. Allgäu or Weilheim i. Oberbayern), DB will name the station using the qualifier in brackets (so the above become Limburg(Lahn), Kempten(Allgäu) and Weilheim(Oberbay) – long qualifiers like the last may be shortened). Therefore, when looking for a train to Limburg a. d. Lahn, one would search for a trip to
Limburg(Lahn) in DB’s list.
In case that is not enough to tell stations apart or in case the town name includes or used to include bei (near), this is explicitly given as a b within the brackets as for
Limbach(b Homburg,Saar) in that drop-down list.
If, however, a city name with a qualifier has multiple stations associated with it, they may or may not all carry the qualifier. So Limburg Süd happens to be in the same Limburg as Limburg(Lahn) but the stations in Kempten are called Kempten(Allgäu)Hbf and Kempten(Allgäu)Ost.
In general, stations in these drop-downs go from important to less important. Limburg Süd is served by ICE trains which makes it important; Limburg(Lahn) is the most important station in the most important German settlement called Limburg and then all the way down to Limbach(Vogtland) these are smaller and less important railway stations.
After having a list of stations, DB often includes a list of bus stops (and tram stops or underground stations where applicable). They might not sell you a ticket all the way to whatever small bus stop there is but if they have timetable data (many buses in the countryside are still DB-operated but even within cities they have a surprisingly good access) they can give you a connection. I’m not sure whether
Limbach(Vogtland) Markt is already a bus stop but I’m willing to bet
Limburg ZOB West is. (ZOB is an abbreviation for zentraler Omnibusbahnhof or central bus station – train stations are practically never named that; if anything, a ZOB was built close to an existing train station.)
If you are looking for the city centre candidate, the top station on the list is usually the one you want but in Limburg’s case you’re looking to go to the central station which is