Laune
The word »Laune« comes from the latin word »luna« that means »the moon«. So it has the same origin as the English word »lunatic« (»Verrückter« in German), the Italian »lunatico« (engl: »moody«, ger: »launisch«) and the French »lunatique« (same meaning as the Italian word).
The original meaning of »Laune« was the mood of a person, that was influenced by the moon. It was used to describe that part of a persons personality that often changed without any noticeable reason.
This origin is mostly forgotten now, but still »launisch« can be best translated into English as both, »moody« and »capricious«. It also means »wayward« and »petulant«. So »launisch« has a negative connotation, and the noun »Laune« often (but not always) also has this negative flavour:
Mann! Der Chef hat heute aber wieder eine Laune!
Was meinst du, wie er reagieren wird? Man weiß ja nie wie er bei Laune ist.
If »Laune« is used in a positive context, you always need other words to add this positive mood:
Heute zahle ich, ich bin gerade in Spendier-Laune.
Herzlich willkommen bei Gute-Laune-Radio, dem Sender, der sie den ganzen Tag bei Laune hält.
And Laune means something, that can change rapidly without a noticeable reason. This is not true for:
Stimmung
This word has a very different etymology. It comes from the word Stimmung (englisch: »tuning«) that describes the tuning of a music instrument (piano for example).
So, if all parts of your life fit well together in a harmonic way, your Stimmung is good. If you feel some dissonant aspects, where things do not fit together, and where parts of your life are under stress, then your Stimmung is bad.
This musical origin is also forgotten (like nobody remembers the moon when talking about Laune), but it still influences the meaning of the word.
The tuning of an instrument doesn't change very rapidly. Think of a piano: Once tuned, it keeps its tune for many months and years. This is also true if it is mistuned: This state lasts on very long.
So Stimmung is very similar to Laune, but describes something that is more stable. Stimmung doesn't change within seconds or minutes, Laune does.
Jürgens Stimmung ist bedrückt. Schon seit Wochen wirkt er so depressiv auf mich.
Gabi verbreitet immer eine fröhliche Stimmung. Jeder freut sich, wenn er sie sieht.
So you can think of Laune as the volatile part of mood, while Stimmung is the more basic and stable part of it.
There is another difference: Laune is an attribute of individuals. Groups don't have Laune (but every single member can have »gute Laune« or »schlechte Laune«). But Stimmung is something that both, individuals and groups can have. But usually you don't say »the group was in a certain mood«. A group usually meets at an event, and so you say »at the event was a certain mood«, but what is meant is the mood of the group:
Bei dem Konzert war eine tolle Stimmung.
Die Stimmung beim anschließenden Essen war noch bedrückter als beim Begräbnis selbst.
