Difference between 'funnier' and 'more fun'

[Ana]

Test No. errors/inter-3 "Sally and her Letter", question 3

It is much more funny if you can share an amusing experience with someone you know well.

(a) more funny
(b) share
(c) with
(d) well

Test No. errors/inter-3 "Sally and her Letter", answer 3

It is much funnier if you can share an amusing experience with someone you know well.

Correct entry: funnier
The error was: (a) more funny
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What's the difference between more fun and funnier?

[Alan]

Funnier is the comparative form of the adjective funny. More fun means literally a larger amount of fun where fun is a noun.
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English as a Second Language
You can read my ESL story 'the' vs. 'a/an'