Hmmm... Could we agree that the two terms are very close in meaning?
The Latin root of "innate" indicates that "you're born with it" and that it
is not "derived from experience"*
The Latin root of "intuition" indicates that "you look at it and know it";
i.e. It is "instantaneous apprehension"* that occurs "without the conscious
use of reasoning"*
(* I'm using an ancient Webster's for reference)
In terms of practical human experience it's kind of difficult to separate
the two concepts, even tho the root definitions differ.
As for my nipples, ....well....
My newborn son "understood" his mother's nipples without hesitation. I
don't know that he really felt the same way about mine. Note: He could
also be easily fooled/distracted/satisfied by a plastic nipple.
That same son now easily plays complex computer games that have an
"intuitive" interface. I believe that his ability to do so is the result of
experience (with other games and logical structures, social norms, media,
etc.), though *without* the conscious use of reasoning.