Am an expat student in the U.S., Am I going to get the same student benefits and discounts in the U.S. just like the local students using my student ID?
Ultimately it is up to the individual company or venue to set whether or not they make a distinction between domestic or international students but I am yet to find one that does.
From Carnegie Hall:
Buy your tickets at the Box Office on 57th Street and Seventh Avenue. A student photo ID is required for purchase of up to two tickets.
which means that as long as your student ID is valid you should be able to obtain a discounted ticket.
In addition I would think that making a discount/service limited based whether the student has residency in the US or not is likely to bring a constitutional challenge to such limitation but IANAL.
The easiest way to get around the problem is to get an International Student ID card. You have a lot of information in: http://www.isic.org/ They also connect you to sites that offer discounts. Quite useful.
From my experience in a state accredited private University, as a foreign student I was not eligible for any financial aid or (of course) discount on tuition. Anything that required a student ID though is the same for everybody in my experience: foreign students are issued the same Student IDs as everybody else.