I aso disagree a bit with Alan, all cases of T1 are not autoimmune,
The aetiological type named Type 1 encompasses the majority of cases which are primarily due to pancreatic islet beta-cell destruction and are prone to ketoacidosis. Type 1 includes those cases attributable to an autoimmune process, as well as those with beta-cell destruction and who are prone to ketoacidosis for which neither an aetiology nor a pathogenesis is known (idiopathic). It does not include those forms of beta-cell destruction or failure to which specific causes can be assigned (e.g. cystic fibrosis, mitochondrial defects, etc.). Some subjects with this type can be identified at earlier clinical stages than "diabetes mellitus".
http://www.staff.ncl.ac.uk/philip.home/who_dmc.htm
So T 1 involves autoimmune destruction, but also destruction of beta cells for an unknown reason. T1 is prone to DKA.
TIa is definitely autoimmune,
T1b is we dont' really know why, maybe an antibody we haven't found, maybe something else but they've lost their beta cells and will go into DKA without insulin.
Some people have beta cell destruction for another reason ie a disease or a genetic defect or a physical destruction of the pancreas. These people are neither T1 or T2: they are officially 'other types'.
So what do you classify a person who is insulin resistant, gets diagnosed in DKA, need insulin but is found to be very insulin resistant and then after a few months seems to get better. They then stay Ok, maybe for years and then it happens all over again. What type are they?
(answer: ketosis prone type 2 or type 1b, or atypical diabetes dependent upon who's writing)
As posted already the definition for T2 is also very wide
The categories are just boxes designed by a commitee and we don' all fit into them easily. The more they find, the less well the boxes fit. (and it's probably about time for a revision but some doctors still haven't got used to this one as its only 12 years old)