A chatbot answers, an agent acts
A plain chatbot takes a message and returns a message, it's a single request-response exchange with no persistent goal and no ability to affect anything outside the conversation. Ask it to book you a flight, and the best it can do is describe how you might do it yourself. An agent is different because it can plan a sequence of steps toward a goal, use tools to take real actions, like calling an API, running code, or browsing a webpage, and adjust its plan based on what those actions return, all without a human manually executing each step in between.
The defining trait isn't the underlying model, the same model can act as a chatbot in one setup and an agent in another. What changes is the scaffolding around it: does it have access to tools, does it have a loop that lets it take multiple actions in sequence, and does it have a way to check whether it has actually achieved the goal, or does it just produce one message and stop.