Type 3 or Type 111 refers to other types of diabetes (other than T1,T2 and gestational) It includes diabetes caused by different genetic conditions, diseases, damage to the pancreas, infections, drug induced. There are a lot of different known causes, some extremely rare.
A World Health commitee on the diagnosis and classification of diabetes (think it was 1999) used 4 sections, other types was section 3 and that was subdivided into 3a to 3h.
The Americans version ( which was easier to find edit : it has a link to the WHO version which was 1997) uses the same classification but a Roman 111 rather than a 3. It has sections A-H
see table 1 Etiologic classification of diabetes mellitus
http://care.diabetesjournals.org/content/27/suppl_1/s5#T1
The only one that seems to have ever been used much is 3c for diseases of the exocrine pancreas. e.g. MODY tends to be called MODY not 3a.
Later researchers suggested that alzheimers may also be another form of diabetes .I don't know though whether, whoever first suggested it realised that there were already many different types under the T3 heading