Almost every prescription drug which is sold through a pharmacy these days is a branded, labeled drug. This means, for example - that you are actually buying a chemical compound, which has been disguised as a unique, copyrighted substance. In reality however, the truth behind each of these drugs is that you can indeed buy them for a lot less money - without the fancy brand name.
This is indeed true for the commonly prescribed sleeping pill - Ambien. The main active ingredient in Ambien is a chemical named "Zolpidem" - which is actually the substance which allows you to fall asleep faster. Therefore, as you can see, Ambien becomes not the actual drug itself, but simply a marketing name for which the company can claim is theirs.
If generic Ambien is indeed available and readily produced, is it possible for a normal consumer to swap their prescription for Ambien in to the generic version? Indeed, this seems to be possible in a number of jurisdictions. In fact, if you live in a country where the government subsidizes your prescriptions to some extent - you may find that you are only able to get the generic version of the drug subsidized - and not the version with the "marketing brand" label.
If the government does not play a part in subsidizing your medications - you might still be able to swap the prescription for "Ambien" in to the generic Ambien for. This will almost certainly depend on the policies employed by your pharmacist - so it is worth asking when you go in to get your prescription filled.
To answer this question as simply as possible - the answer is no. Generic Ambien is exactly the same as the branded product itself, because they are both based off the same active ingredient.
Of course the support, documentation, and other services that you would expect from a pharmaceutical company will probably not be accessible to you if you decide not to pay the extra for the branded version - however then again, if you have been taking Ambien for the last few years, you probably already know exactly how to take it, what the risks are, and what not to do - so these additional services will most likely not be utilized anyway.