There is a very simple and obvious definition: it's agentic if it uses tool calls to accomplish a task.
This is the only one that makes sense. People want to conflate it with their random vague conceptions of AGI or ASI or make some kind of vague requirement for a certain level of autonomy, but that doesn't make sense.
An agent is an agent and an autonomous agent is an autonomous agent, but a fully autonomous agent is a fully autonomous agent. An AGI is an AGI but an ASI is an ASI.
Somehow using words and qualifiers to mean different specific things is controversial.
The only thing I will say to complicate it though is if you have a workflow and none of the steps give the system an option to select from more than one tool call, then I would suggest that should be called an LLM workflow and not an agent. Because you removed the agency by not giving it more than one option of action to select from.
Agentic AI comes out of historical AI, systems computing and further back biological/philosophical discussion. It's not about tool use although ironically, animal tool use is a fascinating subject not yet corrupted by the hype around intelligence.
I implore you to look into that to see how some people relate it to autonomy or AGI or ASI(wrongly, imo - I think shoehorning OOP and UML diagrams plus limited database like memory/context is not a path to AGI. Clever use of final layers, embeddings and how you store/weight them (and even more interesting combinations) may yield interesting results because we can (buzzword warning) transcend written decoding paradigms - the Human brain clearly does not rely on language).
However what gets marketed today is, as you say, not capable of any real agent autonomy like in academia - they are just self-recursive ChatGPT prompts with additional constraining limits. One day it might be more, but libraries now are all doing that from my eye. And recursion has pros but emphasizes the unreliability con/negative of LLMs.
That's not the definition I see most people using. Plenty of tool calling going on purely to structure an output, which could also be achieved by prompting.
For me, agentic means that at least at some stage, one model is prompting another model.
This is the only one that makes sense. People want to conflate it with their random vague conceptions of AGI or ASI or make some kind of vague requirement for a certain level of autonomy, but that doesn't make sense.
An agent is an agent and an autonomous agent is an autonomous agent, but a fully autonomous agent is a fully autonomous agent. An AGI is an AGI but an ASI is an ASI.
Somehow using words and qualifiers to mean different specific things is controversial.
The only thing I will say to complicate it though is if you have a workflow and none of the steps give the system an option to select from more than one tool call, then I would suggest that should be called an LLM workflow and not an agent. Because you removed the agency by not giving it more than one option of action to select from.