Hoarseness is the name of the state: the roughness in the voice. If you have hoarseness, your voice is hoarse. Doctors use this word a lot — they will ask how long the hoarseness has lasted, because a voice that stays rough for weeks is a reason to get checked. Everyday speakers more often say 'I've got a hoarse voice' or 'I've lost my voice' than 'I have hoarseness,' which sounds a bit like a clinic. You will still see it on medicine packets and in sick notes. It is a slightly more formal, 'condition' way of talking about the same thing as hoarse.