I will break my assistance down into two parts, Windows 7 upgrade related, and then OEM vs. Retail related. I haven't seen what was given to you, but I believe what you received was what is actually known as a "Not For Resale" or NFR copy.
First, with respect to the upgrade from 7 to 7 Ultimate (all credit goes to windowsteamblog.com for "step-by-step"):
The Windows Anytime Upgrade Experience for Windows 7
When a customer launches Windows Anytime Upgrade (WAU) from Windows 7, they are presented with 2 options: purchase a WAU product key online or enter a WAU product key from a WAU retail package purchased in a store.
If a customer has a WAU product key, they will choose "Enter an upgrade key" to proceed with the upgrade.
Customer will enter their WAU product key.
The WAU product key the customer entered will be verified as valid.
NOTE: Step 2 and 3 do not happen for people who choose to purchase a WUA product key online. The process of buying a WUA product key automates these 2 steps and takes you directly to Step 4 after the purchase. After making a WUA purchase online, you are given the ability to print out a receipt and are also sent a copy via email.
Customer will accept license terms to proceed.
Customer will be asked to save their work and close all programs. To proceed, the customer will click the "Upgrade" button.
The upgrade takes place! The customer's PC will reboot.
The upgrade finishes and the customer is now running the version of Windows 7 they upgraded to with all its features!
With regard to OEM vs. Retail:
Retail versions of OS's are known as "vanilla" in that they can be installed on any machine that meets the minimum system requirements for the installation. OEM (Original Equipment Manufacturer) versions are usually customized by the OEM for their specific hardware platform or "footprint" and will actually stop installation if the hardware doesn't match what the OS is expecting. Manufacturers like HP and Dell have "hardware signatures" which are looked for during the installation process which assist in determining if the OS will install or not.
OEM versions of software such as MS Office and the like are a different story. Generally, the only difference between Retail and OEM is that the OEM version has the product key imbedded in the installation, negating the need for user input. This is not a hardfast rule, but is a generallization.
I hope this helps.