What is a 3rd party program? In regards to UO, a 3rd party program is one that is created by someone other than OSI/developers of UO. There are only a few 3rd party programs that are considered "legal" by OSI. These programs are rated "UO Pro".
OSI has determined that only a few programs are ok to use with UO, and are listed on the UO Pro webpage. By using any other 3rd party utility, you run the risk of getting your account banned. Technically, almost every program on your computer is considered a 3rd party program. From icq to your firewall (if you run one) to internet explorer. However, using any of these programs will not get you banned.
Any program that interacts with the UO Client needs to be UO Pro in order to be safe. UOA and UOF/UOE (UO Freedom/UO Extreme) both interact with the UO Client. However, UOA is UO Pro, and UOF/UOE is not. While they are essentially the same program, using UOF/UOE can get you banned from UO. However, any screenshot utility or calculator program (like the Taming Utility, Smith Calculator, or Alculator, etc.) is completely safe to use without UO Pro status. None of these programs interact with the client or the servers.
Where should you download 3rd party programs? Always always get the program from the people who created it. I don't care if it is your guild page or what. There's no telling where the webmaster got it or what sort of "customizations" have been made to the program that could void it's UO Pro status. Getting it directly from the creators also ensures that you avoid any virii that could accidentally be distributed by unknowing webmasters.