I've long noticed that LEO and Duden don't get slang and jargon quite right; there is very little if any overlap. Perhaps they have been misled by some English dictionaries that collude with the confusion.
Used properly (and I would have thought almost universally):
a type of language that consists of words and phrases that are regarded as very informal, are more common in speech than writing, and are typically restricted to a particular context or group of people.
Me: But not especially, if at all, a group of technical or professional people.
an informal nonstandard vocabulary composed typically of coinages, arbitrarily changed words, and extravagant, forced, or facetious figures of speech
special words or expressions that are used by a particular profession or group and are difficult for others to understand.
the technical terminology or characteristic idiom of a special activity or group
Me: This is more or less [fachsprachlich] but could possibly be stretched to include some other cohesive groups although not, say, young people generally. Don't misuse it to mean slang; it is often but not necessarily at least a bit disparaging; sometimes it is used as a very disparaging term for the jargon of some such professional or technical group (e.g., lawyers or insurance contracts), as in:
obscure and often pretentious language marked by circumlocutions and long words
Me: The last example tends to be used for text/language in context rather than for individual words.
In other words, the #1 Duden definitions from the OP get it about right (omitting the incorrect [umgangssprachlichem] aside); it's pushing the #2 definitions too far that go off track.