German language usage - Dom or Münster

According to wikipedia

Freiburg Minster was not the seat of a bishop until 1827, long after it was built.

So I guess they had called it Muenster for 600 years, they decided not to change its name "cathedral" after it became one.

Ulm Muenster is a Lutheran church, thus not a cathedral.

The church in Frankfurt, St. Bartholomews, is called the Kaiser Dom, but was never a Bishops seat, so not really a cathedral. Because the Archbishops were there all the time though, for elections and coronations, it got the nickname of being a Dom and everyone calls it that.

Do not look for a dome in these cathedrals, though they may have one.
Dom is short for Domus Dei, or House of God and means it is a Bishops' seat.

The difference is (1) etymological and (2) regional. In both cases, however, a concept expansion occurs, which brings the words semantically closer together.

Dom is borrowed from French dôme, where it had developed as a short form of Latin domus dei ("house of God"), i.e. the church of the bishop, the local representative of God. After the Reformation in Germany, many cathedral churches lost their episcopal seat and status, but the name was retained. So, "Dom" expanded to desing a "large / significant church".

Münster goes back to Latin monasterium, "monastery", and originally denoted a bishop's see occupied by an - often Anglo-Saxon - monk and administered by its monastic community (German "Bischofskloster", an early example is Eichstätt in Bavaria, since 741). When this form of a bishop's see was suppressed as a result of competition from the nobility, the "Münster" initially became the designation of the episcopal church in general and then, as in the case of "Dom", simply a reference to an important church. E.g., the Ulm Münster, which was a prestige project of the citizens and never a monastery or bishop's church, has been called "Münster" since 1465, almost 100 years after construction began. Moreover, the word is almost completely confined to the speaking area of Upper Germany (Oberdeutschland, i.e. southern Germany, Austria, and Switzerland). I believe that English minster has experienced a similar development of meaning.

thanks all. I love to understand these things.

And to throw one more question into the ring - there's also the Basilica, such as in Trier. I understand that that is so because its Roman heritage.

I (native-speaker of German) don't really think about the technical difference when I think of the words, although I know that there sort of is/was one in some cases.

For me, it is just that some are Dom and some are Münster. It feels mostly regional to me, I think -- more Münster are for me associated with BW and Bayern.

From my understanding of church descriptions, a Basilica means the 2 side naves are half the height of the main hall. For example, there is the Einhard Basilica in Seligenstadt, first built by the biographer of Charlemagne.
It doesn't have anything to do with the Romans.
I may very well be wrong on this one, but it is early morning and just started my 1st cuppa coffee.

Re- 'Basilica'

The word basilica is derived from a Greek term meaning “royal house.” In the Catholic world, a basilica is a church building that has been accorded special privileges by the pope. There are two kinds of basilicas. The world’s four major, or papal, basilicas are St. John Lateran, St. Peter, St. Paul Outside the Walls, and St. Mary Major, all in Rome.
Minor, or lesser, basilicas are significant churches in Rome and elsewhere in the world that meet certain criteria and are given special ecclesiastical privileges. Minor basilicas are traditionally named because of their antiquity, dignity, historical value, architectural and artistic worth, and/or significance as centers of worship. A basilica must “stand out as a center of active and pastoral liturgy,” according to the 1989 Vatican document Domus ecclesiae: Norms for the Granting of the Title of Minor Basilica.
https://stspeterandpaulbasilica.com/what-makes-a-basilica

(Replying as a native German speaker:)
Unlike Dom and Münster, Basilika has always remained a loan word in German and has retained the two meanings of the original language, Latin (which in turn took it over from Greek basiliké stoá, "king's hall"):

(1) A church building with an high nave, two lower side naves and an apse. This structure is derived from the Roman basilica, an administrative building of the type of the Basilica Iulia, the ruins of which are still standing on the Forum in Rome. The ecclesiastical prototype is the Basilica in Laterano, built by Emperor Constantine, who translated the formal language of the representative state building to the church architecture. This structure is historically the most common, even if it is obscured by architectural fashions, e.g. in the south German Hall Gothic by aligning the height of the side aisles to the main nave (some forum members surely know the example of Dinkelsbühl) or in the Baroque by subdividing the central nave into several ellipsoidal or round building elements (as in Johann Michael Fischer's splendid basilica in Ottobeuren).

The basilica in Trier retraces, as it were, the "translation process" mentioned above in its history, because it was initially an audience hall of the Roman emperors (Trier was, after all an imperial residence of the western empire in late antiquity, along with Milan). After the residence was abandoned, it was converted into a church.

(2) A papal honorary title for a church, fully basilica minor (cf. the posting of @joe32F above), which is independent of the form of construction. There are just under 2000 basilicae minores worldwide.

(Please forgive my long diatribes, but I am also interested in these things.)

Here is a nice article:
https://www.swr.de/wissen/1000-antworten/dom-muenster-kathedrale-basilika-was-sind-die-unterschiede-102.html

The highlights:
Dom is a generic term for an important or impressive church building. A cathedral is a bishop's seat. Therefore it need not be architecturally important, though most cathedrals are also Doms (like Köln). Minsters are those that at some point had attached monasteries, though the term became common even for those without an attached monestary. Basilica have certain architectural features--unless, of course, the Vatican bestowed the honorary title of basilica on the church. However, all this should be taken with a grain of salt as Catholicism vs. Protestantism as well as regional histories (changing religions, political allegiances) and regional linguistic differences all played a role.

In other words, there are theoretically differences, but there are so many exceptions that there really aren't.

Unless you are in Hamburg--then the Dom refers to the big carnival that comes three times a year with rides and games and not to any of the impressive churches. Because of course it does (there actually is a reason, but who needs to hear all of that!?).

A good historical and cultural question.....the easiest way for me is to just commit them correctly to memory, be it in Aachen, Ulm

Erfurt, Worms, Straßburg, Naumburg, Magdeburg, Koeln, or Mainz.

In Berlin all three are characterized as "Dom"