Is there a difference between hot food and spicy food and hot and spicy food?

Yes, hot food is hot because of the temperature while hot, spicy food is like that because of the spices & it's temperature. 

Not really i think. .

Difference between heat [temperature] and heat [spiciness]. Many hot [spicy] foods are normally served hot [temperature]. Example curry.

Yes, hot food is gauged by temperature and spicy food is gauged by scoville units. 

Hot (if you aren't just refering to the temperature of it) normally refers to the amount of chilli in it.

Spicy can mean any kind of spice (so there may not be any chilli in it at all).

Picante vs caliente. Picante has spicy peppers in it. Caliente causes blisters.