Its a HUGE difference and one that I have unfortunate experience with.
Authorship means that your name will actually be listed as one of the authors, which is searchable in any publication database. What order you are in will depend on your contribution and the ego of the PI, but it is much more impressive.
Getting mentioned means that there will be some tiny type 4 font, usually at the end of the article which says something like, "The authors would like to thank boxasaurus for his contributions to this work by picking up our laundry and washing the glassware."
Students need to be aware that a lot of trickery goes on in labs; PIs know that your goal is often publication to improve your CV, your chances at medical school, etc. The trouble is, that sometimes they have no interest in helping you do that or for whatever reason, so they "stretch the truth" and tell you, "you'll be on the article" or use other such vague comments. You need to be specific about what that means for you, and accept whatever it is, depending on your goals. They rely on your cheap labor.
In case it wasn't obvious, I spent years in a certain Neuroscience lab, only to come out with a couple of measly pubs, and of course, many many "mentions of gratitude". At the end, the current Neurology fellow was so disgusted by what he saw, that he actually apologized to me and told me how embarassed he was to be associated with them, even if the issues had long been a problem before his arrival. And it wasn't just me; this happened to many friends of mine, all over the country.
So yes, the two terms are totally different.
