Bocsánat is more formal/polite than bocs. In fact, bocsánat itself is a noun, and it means forgiveness or apology. So, bocs is just a shortening of the word.
There are several expressions using bocsánat, like bocsánatot kérni (= to ask for forgiveness) or bocsánatot nyerni (= to be forgiven)
Thanks a lot! I just figured someone could ask these kind of obvious questions, since the course was just released. I always like to dive right into understanding the mechanics of a given language even if it is at first learning kind of frozen phrases like greetings and expressions.
I guess it depends on the company. Personally, I prefer 'bocs', because it's short and simple, while I find 'bocsi' too cute. That added '-i' is a diminutive suffix, and for me, saying 'bocsi' is less of a serious apology than 'bocs'. and both can be said with the right uncaring attitude to imply that the other one is a fool ;)