The original classifications for LTs were developed by BITA for statistical analysis purposes. BITA report on manufacturers' sales performance to Government, and are UK representatives on various international standards bodies.
When ITSSAR was first set up in the BITA office of the day, they adopted the BITA classifications for identifying training. Over time, additional classifications have been added. For example, I got the pivot-steer and the vehicle-mounted truck classifications added when I worked for ITSSAR. I also sought the 5,000kg limit for counterbalanced trucks (raised from 3,000kg). After AITT split from ITSSAR, AITT continued to use the same classifications for training purposes.
Later, when I worked for RTITB, I adopted similar weight and stack height classifications for the purpose of consistency in operator training registration, although I didn't adopt the BITA names.
The principles of operating trucks of different weight or stack height categories will essentially be very similar. progress can be made from one to the other generally by conversion or familiarisation training, as one would do for transfer from one power source to another. It will be important to record and certificate such additional training. the actual type of training and the duration required will depend upon the size of truck involved and the type of work it is expected to perform.