When driving in New York, do you have to full stop in a red light and wait to turn right when it is green?

I want to know that when driving in New York, do you have to stop at the red light and wait to turn green then you go right? I am from Canada but I am not sure of the rules and laws in US as for many of us in Canada, we can turn right when it is red but you must full stop first. In New York, I notice some cars would full stop and then wait for green to turn right? What about Niagara Falls like near Lewiston area?