Atkins diet is A ketogenic diet, but not all ketogenic diets are atkins. A keto diet is a diet where energy utilization shifts away from glucose use and towards ketone and free fatty acid use. To be ketogenic diet carbs must be below 100g a day. Atkins induction diet is generally ketogenic since carbs are around 20g a day and you are allowed to eat protein and fat. Atkins is a quack and gets most of his facts wrong. He doesn't believe that calories count, believes in a magical fat mobilizing substance in ketosis, misrepresents the studies where water is lost, not fat, etc. I can go on but he isn't a good example of a good keto diet source. Also, a high fat intake isnt necessary for ketosis to develop, its the absence of carbs as well as not overdoing protein. i can go on but heres a real quick explanation. Let me know if you need more details.
For bodybuildiers/lifters there is a SKD, TKD, and CKD.
SKD (standard keto diet) is a strait keto diet w/ no carb ups, similar to atkins type diet.
TKD is a targeted ketogenic diet, where carbs are ingested around training.
CKD is a cycling ketogenic diet where you eat low carbs during the week, and carb up on the weekends.