A "funny animal", in practice, is an anthropomorphized animal, though the
 usage tends to lean more toward more "cartoony" characters, and does not
 carry the same wide, sweeping connotations that "furry" seems to have. 
 (e.g., I don't usually hear centaurs and anime cat-girls referred to as
 "funny animals")

 Some writers and artists who claim the term "funny animals" for their
 subject matter don't necessarily consider themselves "furry", though on
 the surface this might seem to be almost a synonym.  This is largely
 because of the baggage the term "furry" carries with it, as a number of
 people see "furries" obsessed with the sexuality of their fictitious
 characters.  A "funny animal" is not necessarily a character in solely
 humorous situations, and not necessarily restricted to Saturday morning
 cartoon antics.  The "funny" part of the term seems to more apply to the
 fact that these characters are not like *real* animals.