Photo- you veg your plants with either 24 hours of light or 18 hours of light & 6 hours of darkness and you need to switch them to 12 hours of light and 12 hours of darkness during your flowering period to induce to the plant into budding.
Auto- you veg and flower with no light change, you can start your seeds with 24 hours of light and take them all the way to the end of the flowering cycle without switching your lights. some people do 18/6 the whole time. there's a few different light cycle choices it seems everyone has there own personal preferences.
I'm not sure about the nute difference with the auto, i assume you would still use nutes during veg and flowering....i got a free auto with my all the photos I ordered from attitude and have yet to plant it.