Camilo
There's no such thing as Modular vs Integrated on the FAA side, one could say that there are similarities with Part 61 vs Part 141 but it's still quite different. I believe that as a non US citizen nor legal resident you have to attend specific FAA schools that are approved for instructing foreigners, those schools are Part 141 (Except a tiny school somewhere in California that is Part 61 but that doesn't matter here) The courses in those schools are a bit more structured and you can complete your training in less hours provided you are proficient enough. There are tons of posts on this forum about the differences between Part 61 and 141 with much better information.
The add-on course you are referring to describes a course that an already certificated Pilot rated in one category (Airplane for instance) would take in order to get rated in another category (Rotorcraft Helicopters for example). That can happen at any level: Private, Commercial or Airline Transport Pilot, Flight Instructor and the Instrument Rating as well. I hope this helps and can only recommend you research more what has been posted previously.
