Hello ruby6132,
Welcome to the HP Forums! I hope you enjoy your experience!
I understand there is a discrepancy between what HP Support Assistant shows and what HP Updates shows. I understand that this is confusing, and I will do what I can to assist you!
First, I need to ask if you have an HP printer installed. This is because HP Update might be connected to your printer, if one is installed. That would obviously show difference, since it would be showing printer updates.
Regardless of whether or not that is the case, HP Support Assistant should be uninstalled and reinstalled. The reason for this is because failed updates are never a good thing. The program may need to be refreshed to bring it up-to-date and to resolve any issues it may have.
Since the program came with the computer, you can use HP Recovery Manager to uninstall and reinstall Support Assistant properly. For more information on how to do this, please reference this document: Using Recovery Manager to Restore Software and Drivers (Windows 7)
I believe this step will help you out. Either way, please provide your results. Thanks for bringing this issue to the HP Forums. Have a great day!
Mario