What is the difference between "intermediate" and "intermediary" when both mean the same thing? [closed]

I have a tendency to say

1. This case is intermediary
2. This case is an intermediate one
3. This is an intermediate case

I probably would stumble over

4. This is an intermediary case

and come to a halt at

5. This case is intermediate

Grammatically there seems to be no difference: both are adjectives (and, according to Merriam-Webster, in this context both even mean exactly the same thing).

In other words, I seem to prefer intermediate for modifying a noun, but intermediary for predicating it. Is there any rationale for this preference, or can/should I use intermediate and intermediary interchangeably¹?

_{¹ Only when they mean the same thing, of course.}

Oxford Learner’s Dictionaries, broadly backed up by Google Books, does not agree with you: this case is intermediate is fine; this case is intermediary is not.

Merriam-Webster gives intermediate as a synonym for intermediary, but Oxford Learner’s does not: it defines intermediary as go between only:

1 a person or an organization that helps other people or organizations to make an agreement by being a means of communication between them

→ SYNONYM go-between, mediator

● Financial institutions act as intermediaries between lenders and borrowers.
● All talks have so far been conducted through an intermediary.

→Intermediary adjective [only before noun]
● to play an intermediary role in the dispute

On intermediate Merriam-Webster and Oxford agree (Merriam-Webster):

1 : being or occurring at the middle place, stage, or degree or between extremes

2 : of or relating to an intermediate school <an intermediate curriculum>

Google books shows that usage conforms to Oxford’s definition. We likely have a lot more cases that are intermediate between mild and severe than go-between cases, and as we would expect Goodle Ngrams shows intermediate case 40-50 times as frequent as intermediary case. Raw Google gives seven instances of case is intermediary only (which violate Oxford’s only-before-noun prescription), two of which are your post’s; but it gives 150,000 instances of case is intermediate. You can have go-between roles, and Ngram shows intermediary role six times as frequent as intermediate role of late.