Atkins is the Keto diet - no difference. Severely cutting carbs to get your body in a ketogenesis is the same process no matter what it’s called.
Atkins was a pioneer in that he popularized it and was, obviously, a doctor, which helps on the uptake of the idea.
All the differences are splitting hairs.
If you are doing Keto, do NOT buy those Atkins meals at the supermarket, they will put you out of Ketosis.