I was being diplomatic in my response above, having spent a few years as a US govvie mkt maker/book runner at a NY primary dealer bank, I am not too bad at the bill/bond/futures/basis lark!
We do need to correct these things quickly, so that some poor soul doesn't take the info into their already overloaded memory bank, ahead of the big day.
T-bill --> maturity less than one year. No conversion.
T notes --> maturity 1-10 years --> conversion.
T bonds --> maturity 10+ years --> conversion.
The CTD conversion factor, however, is normally referred to the classic 30 year T bonds futures, although it exists for 2,3, 5, 10 as well as ultra bonds.