If it's of any interest to anybody, here is my understanding of the essential difference between adjectives and adverbs. I'd welcome any comments at all.
Both adjectives and adverbs are ways of describing. They modify by description. Adjectives modify nouns, signifying properties/attributes of things:
The sky is blue.
The chair is soft.
Adverbs modify verbs (events), describing a way of doing/happening.
Open it carefully.
It's snowing heavily.
Of course, adverbs can also modify the verb BE. In this case, they describe a way of being/existing. So in the example
I'm there now.
both there and now describe a way of existing in space and in time (what in ontology can be called the 'ontic properties') of the subject.
Interestingly, adverbs may also modify adjectives,
It's really good.
where they can be understood to describe the ways of having properties.
Based on the above, it's hard for me to understand otherwise as a property of anything. It seems to me to be a way of being (different), and therefore adverbial.