According to theoi, Satyrs are depicted as having:
the tail of a horse, assine ears, upturned pug noses, reclining hair-lines, and erect members.
Another group of 'rustic' spirits called the Panes (after the god Pan of course) were, similarly to the Fauns:
goat-footed men, with the tails, bushy beards, snub noses, pointed ears and horns of a goat.
So in fact the romans Fauns were closer to the greek Panes than to the Satyrs. And it was clear, to at least some latin authors, that Fauns and Satyrs were not similar:
sunt mihi semidei, sunt, rustica numina, nymphae
faunique satyrique et monticolae silvani;
Ovid, Metamorphosis, 1, 192-193.
Of course both Satyrs and Panes were closely associated with one another as they were both rustic spirits, companions of Dyonysos.
Also, it should be noted that, prior to the "Greek mythos transfer", italians had two pastoral god/goddess called Faunus and Fauna. Faunus was later equated to Pan, and it might be at this time that he started being represented with goat horns.