If your "unlimited plan" is not a "blackberry data plan" then the answer is no, they are not the same.
This has been brought up many times, use the red search button above or in my sig and put "data plan" into the search field and see how many results you get on this topic.
Also, see these links to the FAQ's:
What do I need a Data Plan for? - BlackBerryFAQ
Why do I need a Data Plan? - BlackBerryFAQ