"Io sono fra l'uomo e la donna."
There is none, really. Etymologically, "tra" is more appropriate, because "fra" is a shortening of "infra" which meant "below", but that usage has been lost for centuries.
I'm not clear on the essere/stare difference yet in italian but know that in Spanish this sentence would use estar (equivalent of stare) because it's talking about location/position (unless the speaker is proclaiming a sexual identity, which seems unlikely). Can anyone clarify whether it should be "Io sto fra..." rather than "Io sono..."?
In Italian, 'essere' is the 'to be' verb. I am a man is "Sono un'uomo". 'Stare' is also 'to be', but that in terms of HEALTH. For example, When you say, 'Come stai?', it's like saying "How is your health?". You can reply, 'Sto bene', which means 'I am good/well', but in terms of HEALTH. 'Good' as in the adjective would be 'Sono buono' or 'Sono buona', depending on your gender. 'Stare' is also the verb for 'to stay'. Hope this helped!