I don't know exactly which version you purchased, you might have to contact Adobe customer service to confirm. The CS6 products will be available in a few different ways, as perpetual and as subscription. The perpetual versions come in different formats, hard copy (disc in a box) and download, this version includes a serial number and is one which you own. With the subscription version, you are more less renting the product for a set time period, a year, month to month, etc.
Right now the CS6 versions (in either perpetual and subscription) are not available. If you buy a CS5.5 perpetual version currently you can upgrade to CS6 free. This sounds like like what you did and that the free upgrade in this case is a download version.
Upgrades for subscription and perpetual will work differently as well. Subscription customers may get some "feature related" updates before perpetual products. Any updates that address issues with the current release of the software will still be available to both.
The Creative Cloud subscription products are more than just the products themselves and include certain services that go along with them. What specific format, perpetual or subscription works best for you is up to you. If you bought perpetual but actually wanted subscription I would suggest contacting our sales department to see if its possible to change.
There is this Creative Cloud Membership FAQ that has a lot of info about it. It might be helpful if you haven't looked it over already.
Hope that helps,