Artificial Intelligence is the larger umbrella concept under which Robots are designed and built, for specific purposes.
AI is a concept of mimicking human capabilities in machines.
But Robots can have different applications for personal, industrial or healthcare. All these applications require AI, but in a different way.
For example a Humanoid would be a personal assistant for a disabled person and needs to understand daily contextual language and jargons that a PA needs to understand.
An Industrial Robot, on the other hand, will be domain driven, like in SCM (Supply Chain Management or Manufacturing and will need to understand the work scenarios in those domains the way humans do.
Healthcare Robots will need to act as assistants to Doctors and Nurses, understanding medical language and semantics.
Though each of these robots operate differently , they all work under the concept of AI, which is behaving like humans.