A Sugar-Free Diet aims to reduce the intake of added sugar.
Unlike the keto diet which reduces the number of carbs in the final product, a sugar-free diet only attempts to get rid of sugar as an ingredient.
It is not about removing natural sugar such as fructose present in fruits or lactose present in milk.
Since a keto diet is much more restrictive than a sugar-free diet, all keto recipes are sugar-free.
The opposite isn’t true. For example, while an apple crumble can be made sugar-free by excluding crystal sugar, it won’t be keto-friendly.