I am reading from the book by Ken Blacker, 'RT - The story of a London Bus' , which I believe is the definitive work on the subject. It appears that RT 19 was loaned to A.E.C. in its early days for demonstration purposes throughout the country, LT looking to be able to sell chassis to other operators to spread the costs of tooling etc, and during this period the official designation of Regent MkIII (for the chassis) first appeared.
The chassis of RT 19 was modified to a new standard design by A.E.C. in the spring of 1945, being completed by the end of the year. This new chassis was designated 3RT. The body design had to be modified to fit the 3RT chassis, and thus was born the RT3 body.
From then on the RT's chassis designation remained 3RT, but the body designation changed various times as modifications were made, ie; RT3/1, RT8, RT8/2, RT9, but even so, everything remained interchangeable, which is why Aldenham works was such a success* (* my own comment).
I think the abbreviation(s) used in discussion is often just down to personal choice. I would recommend the above book to anyone. If a good copy can still be found, it won't be cheap. I must have baulked at the price, or had a senior moment back in '79, when it was first published about the time of that last day at Barking, as I never purchased a copy at the time and had to spend a hefty amount to acquire a second edition copy in later years, but well worth it.
Just as an aside, did anyone else ever ride an RT round the skid pan at Chiswick works, with the water in play? That was fun, if not a little hairy for the novice
. Never be allowed today, but one of those days I'll never forget.