Hi Hydrazine,
(very) roughly speaking, type 1s can't produce their own insulin, while type 2s can't use the insulin they produce.
A rough rule of thumb taught to doctors is that if the patient is young and has lost weight rapidly, they're probably type 1. If they are middle aged or older and their weight hasn't reduced or has increased in recent years, they are probably type 2.
All kinds of untreated diabetes will produce that thirst/hunger for sugar. Literally eating sugar doesn't cause any kind of diabetes, although eating too much (of anything) and becoming overweight can lead to Type 2 for some people. But it's the overweight thing rather than the sugar that is key to that. Obesity makes it harder for the body to use insulin.
MODY (pronounced MOE- Dee) stands for Maturity Onset Diabetes of the Young and is often misdiagnosed as type 1, as the_anticarb experienced. There are various kinds of MODY, but again roughly speaking, someone with MODY is producing a little of their own insulin still, just not enough to be 'normal'.
Doctors can do a blood test which works out whether you are producing your own insulin. They may have already done that, but it's well worth asking them if they have checked to see if you are MODY. You have a right to know; it's your body.
I would agree with the_anticarb that it's well worth learning the basics on a course like DAFNE, whichever kind of diabetes you have.
And finally - good luck. Not everything about diabetes is bad.