| Jen is probably the best person to ask about this because she's the science wizz. However, the main difference is that ketones are the byproducts of fat metabolism, whereas DKA is a very specific and serious medical condition. When you burn fat, you create ketones. DKA is a form of fat burning which happens because your body simply can't get enough energy from your glucose.
This is a problem for two main reasons. Firstly, DKA makes your blood acidic. Secondly, it also means your sugars are running high. I find it helpful to imagine that the more sugar is in your blood, the more your blood is like sandpaper. All that sugar going round is scraping all your organs, and combine that with the acid...yeah, you're in trouble.
DKA is the reason that people with untreated diabetes die. Depending on the individual, you could be dead within a few days or a few months, which is why A+E usually get involved.
The reason ketones are a problem is because usually, nobody really ends up with ketones in their urine because the body's preferred food source is glucose, not fat. Because ketones indicate fat burning, it could be a result of either DKA or just regular fat burning. Ketones are like smoke - although there's definitely a fire somewhere, the smoke alone can't tell you whether it's a purposeful rubbish bonfire or a house burning down.
Bottom line is, if you find ketones and you're not expecting to find them, then you may have a problem. But ketones alone don't mean that you have DKA - they just suggest its a possibility.  | 
