As an adjective, comic means characteristic or having to do with comedy.1 Comical is a synonym of funny.2 Dictionaries list them as variants of each other, and mixing them up is not an error, but they’re generally kept separate in edited writing.
Both words derive from the Latin comicus, meaning of or pertaining to comedy, and in their earliest uses they were more or less the same. But the words began to differentiate in the 16th or 17th century, and today they are closely related but mostly different in meaning.3 Other -ic/-ical word pairs have undergone similar differentiation—for example, economic and economical, and metaphoric and metaphorical—while others have not diverged in meaning (ironic and ironical, for instance).
In these examples, comic means of or relating to comedy:
Sure, that could work, given a savvy, ” Shakespeare in Love” sort of script and actors skilled in comic subtlety. [New York Times]
His next live show and DVD explores the comic side of daily life in Brazil. [Guardian]
These scenes are a riot, embraced with comic gusto by the delightful actors in Lemoine’s cast. [Edmonton Journal]
And in these examples, comical means funny:
I reckon the supposed levels of their infighting have got so bad it’s almost comical now. [Stuff.co.nz]
This situation was so comical that it prompted Saturday Night Live to parody it. [Forbes]
One frequent and rather comical complaint about London is that the residents don’t chat to each other. [Independent]