Low Carb, High Fat (LCHF) is a different approach to eating than has been suggested for the past 40 years. It seeks to minimize consumption of carbs, moderate consumption of protein and increase consumption of natural fats.
LCHF is very specific about the reduction of carbs and proteins, and an increase in fat consumption for medical benefits (treatment of various metabolic conditions), overall health and weight loss.
Paleo is all about "ancestral" eating, eliminating processed foods and dairy from the diet, and eating more in line with how human beings evolved to eat in our hunter/gatherer period.
They share a lot of features, both attempting to return to a simpler diet where, at the core, there's more of an emphasis on home cooking from natural, whole ingredients. Two main divergence are that Paleo doesn't allow dairy (whilst LCHF encourages it) and LCHF doesn't allow most fruits, except berries (whilst Paleo allows most whole fruits in moderation).
Whilst Paleo generally leads to a lower carb diet (by disallowing many modern foods unavailable to hunter/gatherers), there are no strict limits on carbs. LCHF aims to restrict carbs to between 20g-50g a day, based on your specific goals (weight loss, blood sugar reduction, etc.).