The body has two metabolic states: fed and fasted. The fed state occurs when insulin levels are high while the fasted state occurs when insulin levels are low. In the FED state, the body is in FAT STORAGE mode and "burns" predominately glucose. In the FASTED state, the body is in FAT BURNING mode and burns predominately fat. When insulin is high, it is difficult to lose weight and, conversely, it difficult to gain weight when insulin is low.
When the body is in the FASTED state, the liver makes glucose on demand (gluconeogenesis), which results in relatively low and stable blood sugar levels. Interestingly, insulin lowers the metabolic rate and the difference between the fed and fasted states is about 300 kcalories/day - the equivalent of about 1 hour of normal walking (3.0 mph) for a 180 lb person. A low insulin level puts the breakdown of fatty acids in the liver into overdrive, which results in so much acetyl coenzyme A (acetyl-CoA) production that it overwhelms the citrate cycle in the liver resulting in ketogenesis by forming one acetoacetate from two acetyl-CoA molecules. High rates of fat metabolism can result in up to 50% converted to ketone production. High ketone levels also cause the mitochondria in both brown adipose tissue and white adipose tissue to become uncoupled so that they begin to generate heat like brown adipose tissue, which further increases energy consumption. That might be a welcome side-effect if you've always got cold hands.
In other words, a ketogenic diet is simply one that maintains a low insulin level, which in turn naturally results in ketones as byproduct of fatty acid metabolism.
The three ketone bodies are acetoacetate (AcAc), beta-hydroxybutyrate (BHB or βHB, formed from AcAc), and acetone. However, high serum ketone levels will be excreted in breath (as acetone) and urine (as acetoacetate) "Ketone breath" (sweet or fruity scent) results when the unstable AcAc breaks down into acetone. Ketone breath is noticeable initially as the body shifts to fat metabolism and becomes imperceptible as the body becomes accustomed to burning ketones. Staying hydrated helps to minimize ketone breath. Keto Crotch is not a thing and the rumour may have been started by a diet company or a pasta company, presumably to counter ketogenic diets.
Some in the medical community will warn about ketones possibly causing diabetic ketoacidosis (DKA) but this is nearly impossible to achieve through nutritional fasting because DKA also requires extremely high serum glucose levels (over 13.8 mmol/L or 250 mg/dL) due to insufficient insulin production. Not eating or avoiding carbohydrates generally results in normal glucose levels from gluconeogenesis.
The brain prefers ketones to glucose as its metabolic fuel and will cut back on glucose consumption as ketone levels increase. Ketones are important metabolic fuels for other tissues, including heart and kidney.