A chatbot is usually designed for dialogue. An AI agent is designed for action, such as searching, editing files, calling APIs, creating tickets, or running a workflow.
In practice
The difference is not always strict. Many products start as chatbots and become agentic when they add tools, memory, planning, and permissioned actions.
What to watch
Calling something an agent does not make it reliable. The important question is what actions it can take and how those actions are controlled.