Is there a defined difference between words like "egotistic" and egotistical" or "manic" and "maniacal" in that one could have a manic smile or maniacal laughter and other words that have similar forms?
The OED notes that
[o]ften ... the form in ic is restricted to the sense of 'of' or 'of the nature of' the subject in question, while that in -ical has wider or more transferred senses including that of 'practically connected' or 'dealing with' the subject.
The editors ask us to compare "'economic science'" and "'an economical wife'".
But in many cases this distinction is, from the nature of the subject, difficult to maintain, or entirely unappreciable.
Your example of "manic" and "maniacal" isn't quite parallel here. Both adjectives derive from the word "mania," but the latter has goes through "maniac" and has a long history -- the OED finds a use in print from 1678 -- while the former was invented directly from "mania" in 1921 for use in psychiatry. Nevertheless, as applied to smiles (or laughter), they mean the same thing. Just the way "egotistic" and "egotistical" are little different.
Differences in the two forms do obtain. A well-known example is "historic" (which means noteworthy) and historical (which means of narrative history). But usage dictates the divergence, and there's no general rule to distinguish the difference between the two forms, if indeed one exists.
No there is no defined difference between the words. They are simply different forms of the word.
Maniac is a noun while maniacal is an adjective. While maniac is a person, maniacal describes a behavior or attribute.
Egotistic and egotistical are both adjectives and can be used interchangeably. Egotistic is most common of course.
a noun suffix occurring chiefly in loanwords from Greek, where such words were originally adjectival ( critic; magic; music).
a suffix with the general sense “of the kind of, pertaining to, having the form or character of” that named by the stem, occurring in loanwords