Difference between Unlikely and Uncommon

UNLIKELY vs UNCOMMON: NOUN

Not common or ordinarily encountered; unusually great in amount or remarkable in character or kind
Marked by an uncommon quality; especially superlative or extreme of its kind
Not common; rare.
Wonderful; remarkable.
Not common; unusual; infrequent; rare; hence, remarkable; strange
Rare; not readily found; unusual
Remarkable; exceptional

Such as cannot be reasonably expected; improbable: as, an unlikely event.
Not holding out a prospect of success or of a desired result; likely to fail; unpromising.
Not calculated to inspire liking or affection; not likable or lovable.
In an unlikely manner; with no or little likelihood; improbably.

Marked by an uncommon quality
Exceedingly; very: as, uncommon cheap.
Synonyms Scarce, unusual, unwonted, unique, singular, queer. See common.
Not common; not usual; infrequent; rare; hence, remarkable; extraordinary; strange.

Impossible, Reluctant, Plausible, Inconceivable, Doubtful, Likely, Outside, Remote, Last, Unbelievable, Supposed, Unconvincing, Farfetched, Implausible, Improbable

Common, Rarely, Surprising, Prevalent, Infrequent, Commonplace, Unheard, Special, Unwonted, Especial, Particular, Exceptional, Extraordinary, Rare, Unusual

Impossible, Reluctant, Plausible, Inconceivable, Doubtful, Likely, Outside, Remote, Last, Unbelievable, Supposed, Unconvincing, Farfetched, Implausible, Improbable

Common, Rarely, Surprising, Prevalent, Infrequent, Commonplace, Unheard, Special, Unwonted, Especial, Particular, Exceptional, Extraordinary, Rare, Unusual

Obviously, in my case it is EXTREMELY unlikely.
John Mark might not be unlikely at all.
Spain but I think this one is unlikely.
Discountable effects are those extremely unlikely to occur.
NBA comeback may seem unlikely at this point.
Russia investigation even though his election seemed unlikely.
It indicates the null hypothesis is very unlikely.
Just as people who borrow murder mysteries are unlikely to be murderers, so those seeking information about terrorism are unlikely to be terrorists.
When looking for solutions to problems they are unlikely to arbitrarily rule out any possibilities, even if they may seem unlikely to others.
Responses can be: very likely, somewhat likely, neither likely or unlikely, somewhat unlikely and very unlikely.