You really can not trust catalogues.
In ma,y cases they were photos of mock ups of what the marketing department thought the production department was going to make.
They often depict finishes that never happened.
Like a pearl grey A 10 with a red tank or a black framed B33 with ivory guards, black airbox & oil tank and saphire blue tank.
Now back to the badges.
Rule of thumb, very rule of thumb is the smaller "competition" tanks got the 4" Gold Star badge usually in red and the larger "touring/ road" tanks got the smaller laurel wreath / garter belt / piled arms badge.
The 8 point star badge was new in 60/61 season for the new B40 "Star"
In the UK 62 early catalogue ( Pre-units ) it is shown fitted to both the B40 & C15 road models.
2 months latter in the 1962 A50/65 UK catalogue, the 8 point star is only shown on the B40, the C15 is depicted wearing the comet / pear
The USA East catalogue for 1962 shows only the Spitfire scrambler with the 8 point star on a 3 gallon tank which is the first time it appears on a twin.
The 1964 East catalogue shows the Spit with the 4 gallon tank and Gold Star badges, no modes with the 8 point star badge.
The best refference is the road tests in period magazines and in particular road tests that appear late in the season as they are often done with showroom / demo bikes from the warehouse so are at least real motorcycles and not a photo studio mock up.