Artificial intelligence is the category. Artificial general intelligence is one target inside it. AI covers everything from a spam filter to a language model, and most of it is narrow: skilled at one task, useless outside it. AGI names a system whose competence is not confined to a task.
The practical difference
Ask a narrow AI a question outside its training and it fails, often confidently. Ask an AGI something new and the expectation is that it recognises the novelty, reasons from what it knows, and either solves the problem or learns what it needs. Narrow systems interpolate. General systems are supposed to transfer.
Why people use the words interchangeably
Marketing flattened the distinction. Every product is now "AI", and vendors borrow the word general to imply breadth. The useful test is not what a system is called but what happens when you hand it a problem nobody trained it for.
The short version
AI is a field. AGI is a claim about scope. A system can be world-class at one thing and still be nowhere near AGI, and that is exactly where the industry sits today.