Just to confirm: aparat (fotograficzny)=camera, primarily for still photos
Correct. Although 'aparat' is a very general word, people will be almost sure you mean the one for photos without you mentioning that it's 'fotograficzny'.
If I want to say that I was going to take my camera but left it at home, what I have to say? I mean is there any difference between intentional and unintentional leaving of camera in Polish?
There is no difference between intentional and unintentional leaving of camera in this particular sentence. But you could say: „Zapomniałem kamery. Została w domu” - I forgot to take the camera. It is at home.