There is definitely a usage and etymological dimension to this issue, which I can elaborate on, if you'd like. (It's an issue I come across frequently, and is particularly relevant in regards to original work.)
The use of "Agent" may have arisen partly out of Game Theory, with ideas like "multi-agent systems", possibly because it's quite general (i.e. one does not have to say participant, or player, or actor, etc., and it is species non-specific.)
"Automata" seems to be favored in some circles, and although this term was originally reserved for physical, mechanical devices, it now encompasses a range of physical and information-based systems (with perhaps a contemporary emphasis on the virtual. A famous extension is the categorization of Conway's Game of Life as a "cellular automata". Conversely, "robot" would seem to have usurped "automaton" for physical systems.)
I tend to use agent when I'm thinking in an economic sense, or in a game theory sense as related to computing [see Rational Agent], and automata when thinking in a procedural sense in terms of algorithmic intelligence [see Automata Theory]. But the distinction is partly semantic.
Robot seems to be avoided in the academic literature in regards to information systems, possibly because of the deeply entrenched popular understanding of "robot" as physical automata. The use of the informal "bots" for describe information-based systems seems to have arisen in the public sphere, almost certainly a product of hacker culture, which has a tradition of playfulness. I like the term bots as it is being currently applied, but I feel it has the connotation of trivial (i.e. small and discrete) or massively multi-agent systems, and haven't really seen it used for for "strong" narrow AI.*
Note: "Agent" does not automatically carry the concept of autonomy, although it is sometimes implied. The use of the term is in the sense of "agency" as an action taken by an agent. Agents may be acting on their own behalf, or as proxies.
*"Strong" in relation to AI is a term that seems to be evolving. Initially reserved for Artificial General Intelligence and conscious algorithms, I've seen recent mentions by respected scholars of "strong narrow AI" to refer to recent milestones in Machine Learning. However, the term "strong" and "weak" in relation to mathematics and AI have a history in Combinatorial game theory per the concept of the solved game. Thus, there exist "strong AI" for games such as Nim, Hex, and Tic-Tac-Toe.
Again, there is an element of subjectivity here, but I tend to favor the CGT approach for two reasons:
It's a mathematical definition, unlike the the philosophical definitions ("consciousness" and "humanlike" re: AGI)
Artificial Intelligence is rooted in combinatorial games. [Nimatron may have been the first functional algorithmic intelligence and combinatorial games have been been used as milestones since that time, most notably with Deep Blue, Giraffe Chess and AlphaGo. Non-trivial Combinatorial games are useful because they have simple parameters but complexity akin to nature.
My sense on how "strong" is starting to be used is for algorithms, such as Machine Learning systems, that can outperform humans within a given set of parameters. Thus "strong narrow AI".
The term "intelligence" in highly subjective, and the only functionally meaningful definition I've come across is the concept of bounded rationality.