Well, I would say that when people at the moment say agent they mean what you call autonomous agent. Browsing or code interpreter is just LLM + tool use. I think there is a really large difference in quality between a system that just interacts 1-2 times with some tool/API before giving an answer and one that runs in a loop with undefined length (until it decides to terminate). It's like the difference between programming without loops or recursion vs with them. Night and day.
Currently the loop results in compounding errors and attention failure. Even with reviews, grounding information, and veracity checks in place by other LLMs it still happens.