Ketosis occurs when your body switches from consuming glucose as its primary fuel source to consuming ketones which are generated from the breakdown of fatty acids, either from the diet or endogenous.
Almost all body tissue can run on ketones instead of on glucose, except for certain important tissues like red blood cells, 30% of the brain, retina, some kidney tissue, etc.
For the rest, your body synthesizes the glucose it needs via gluconeogenesis from some protein substrates and from glycerol backbodes from triglycerides. These inputs can be either from the diet or from your fat stores.
Fasting for a few days causes your body to enter authophagy through the inhibition of mTOR in addition to ketosis, so that could account for some of the difference.