Traditional Art category is for original works made with traditional media, or for traditional works commissioned (or requested) by the copyright holder.
Fan Art category is for works that contain copyrighted elements that don't belong to you and that were not commissioned or requested by the copyright holder, even if they were commissioned by a fan. If a work contains elements directly inspired by a copyrighted environment but not representing the original material, like a fan fiction illustration, it still belongs to Fan Art gallery, even if there are your original characters in it.Some subcategories might seem speculative as to where put your work, but in reality it's very clearly specified:
IllustrationsTraditional Art > Paintings > Illustration and Traditional Art > Drawings > Illustration sub-galleries are for illustrations that were commissioned (or requested) by the copyright holder, be it a publisher or the author, and for illustrations to non-fan fiction texts written by you, and for illustrations to public domain texts.
Books & Novels sub-gallery under Fan Art is for illustrations and pictures inspired by a text when you were not commissioned to draw them by the copyright holder and you hold no copyrights to the text itself.
For example: if a publishing house commissioned you to illustrate Harry Potter, you can submit those illustrations under Traditional Art. In any other case - even if you were commissioned by a fan - you need to post the pictures under Fan Art.
PortraitsPortraits of famous people can be placed either in Traditional Art or Fan Art category. But there's a rule to it. Like when you have a drawing of an actor outside his job, you have a choice between Traditional Art and Fan Art category. But if it's the same actor dressed for his role, it can only go to Fan Art.
For example: a drawing of Tom Hiddleston on vacation on the beach - you can submit it to Traditional Art or to Fan Art, but Tom Hiddleston as Loki goes only to Fan Art.