What's the difference between adjuncts and modifiers?

Solution 1:

In short: adjuncts may or may not be integrated into the syntactical structure of the sentence. If they are, they are called modifiers; if they are not, supplements.

There is also a category that includes both modifters and complements, but excludes supplements. These are dependents, which are either complements, or modifiers, or determiners.

At least, this is the terminology used in CGEL; as Edwin Ashworth mentioned in a comment, some grammars use these terms a bit differently.

Discussion

From CGEL:

adjuncts may be dependents (modifiers), … or supplements, elements that are more loosely attached to the clause. (p. 215)

Supplements are parts of a sentence that aren't integrated into the syntactical structure of it, but rather appear as interpolations or appendages (p. 1350):

Pat—the life and soul of the party—had invited all the neighbours.
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