The two terms get used interchangeably, but the distinction matters for what a business should actually expect. A chatbot is reactive -- it responds to what it's asked, within a conversation, and stops there. An agent is proactive within a task -- it can break a goal into steps, use tools, check its work, and keep working until the task is actually complete.
Knowing which one a project actually needs (a better FAQ responder versus something that can actually process a refund end-to-end) changes the entire scope and cost of building it.