That question has bothered me too, so I did a quick search to find something that appears to be clear here:
http://flesl.net/Grammar/Grammar_Glossary/subjunct.php
Here you go:
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subjuncts differentiates them sharply from adjuncts.
One aspect of this difference is the fact that they cannot generally be the focus of certain grammatical operations. For example, adjuncts such as “happily” or “sadly” can be contrasted with one another in “alternative interrogation” in questions such as “Did Harry smile happily or sadly when Jill told him she loved him?” but if an attempt is made to contrast subjuncts in this way as in “Does Jill deeply or slightly love Harry?” the results are unacceptable.
• It is often possible for the same word to act as a subjunct in one context but not in another.
• For example, in the sentence, “Sadly, Sara packed her clothes and left the next morning,” the adverb sadly is acting a subjunct.
However, in the sentence, “Later, Sara spoke sadly about those terrible days,” it is an adjunct, and in “Sadly, Sarah never learnt the real truth,” it is a disjunct.
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...after reading it 10 times... I think it's impossible.
Seriously, I think that it is mainly a matter of word order.
For example, in the sentence:
"Seriously, I think it is maily a matter of word order."
"seriously" should be a subjunct, whereas in:
"I was speaking seriously."
"seriously" should be an adjunct.
In fact, you can ask: "are you speaking seriously or ironically?"
You could even forcibly contrast two subjuncts:
"Seriously or ironically, do you think it is mainly a matter of word order?"
But as you see, they don't really become part of the question. I think that's because "they are not as “central” to clause structure as, for example, adjunct adverbials are".
I think I need an aspirin... :)