Our bodies burn carbs in preference to fats. That is because we only have a limited amount of storage for carbs and we have a very high capacity for fat storage.
We are typically burning some mixture of both fat and carbs (except at extremes). The amount of carbs we are burning is strongly influenced by the amount of carbs we have eaten. If you ate nothing but carbs and ate them at an amount matching your total energy expenditure you will pretty much just burn carbs.
Since most people don’t eat in their sleep there’s some point where the carbs go down and the body starts to draw from the carb stores, aka, glycogen. That can last as long as a day or so but as the glycogen stores draw down the body starts to shift to fat burning. This is known as glycogen sparing.
On a low carb diet our fuel mixture shifts to largely fat based. At very low levels of Insulin that come with a reduction in carbohydrates, our peripheral cells resist the small amount of glucose we produce and we spare the glucose for the parts of our body which rely on glucose for fuel. This is how the low carbohydrate diet is glucose/glycogen sparing.
A high carb diet is fat sparing since it spares our body fat from being burned and reduces the amount of time that glycogen stores are being drawn down.