What is the difference between AI and robots?
Although there are several definitions of "robot", an essential feature of everything called "robot" is that it is capable of movement. This does not necessarily mean displacement; a robot arm in a factory also moves.
There is a single exception to this rule, which is bot-programs like chatbots; I will discuss them later.
Artificial Intelligence does not need to move; a chess program can be argued to be an AI, but does not move.
A robot can actually have AI; one of the definitions of robot is that it is a system, capable of autonomous movement. In order to be autonomous, to be able to make decisions of its own, a certain amount of AI may be necessary.
There is one class of "robots" that does not move, and does not even have physical presence; bot programs, like chatbots, that operate inside systems. I do not consider them robots, because they are not physical devices operating in the real world. A chatbot can be an AI, however - a good chatbot may have some natural language processing to interact with humans in a way that humans find natural.
To summarize; an AI can exist purely in software. But to be a robot, there must be a moving physical component in the real world.
In the broadest sense, the difference is that non-robotic A(G)I may not be possible because, as per this question, it could be that "Intelligence requires a body".
More specifically, it could be that there are limitations to what the traditional (well, 1950s style) 'Brain in a vat' notion of an AI is capable of comprehending, in the absence of experience of embodied experience such as force, motion and "the raw, unawshed world".
First, stop thinking of robots.
A robot is a container for AI,
sometimes mimicking the human form, sometimes not
— but the AI itself is the computer inside the robot.
AI is the brain and the robot is its body — if it even has a body.
the software and data behind Siri is AI, the woman’s voice we hear is a personification of that AI, and there’s no robot involved at all.
In a general sense you can say that robot is a piece of hardware, while AI is software (sometimes hardware too).
Wikipedia states Robot as a machine which performs complex set of tasks automatically.
Machine - A mechanical device basically.
So, technically you can create a robot that doesn't require any kind of complex algorithms to take decisions. A simple line follower doesn't even require a microcontroller. Just some gates are enough. Some other examples of robots are, a robotic arm, automated control systems in industries, etc. If you think about it even the printer in your house is a robot in itself.
Artificial Intelligence is a field of Computer Science which deals with developing systems that can perform tasks rationally as if it is using intelligence (of human level) for taking decisions.
AI deals with complex algorithms. Some examples of AI are speech recognition, face recognition, natural language processing, etc.
AI don't necessarily need additional hardware. A simple desktop at home will work, while the term robot is used for external hardware that does some autonomous task repeatedly.
An AI is a computer program designed for tasks normally requiring human intelligence (a human's ability to learn), while a robot is a machine that completes complex tasks. An AI could be used to control a robot, but they are very different.
Source: Oxford English Dictionary, above links will direct to definitions.