People not working with LLMs often say things like "nope, they just follow stochastic patterns in the data, matrices of floats don't have beliefs or goals". People on LessWrong could, I think, claim something like "they have beliefs, and to what extent they have goals is a very important empirical question".
Here's my attempt at writing a concise decent quality answer the second group could give to the first.
Consider a houseplant. Its leaves are directed towards the window. If you rotate the plant 180 degrees, in a few days it will adjust its leaves to face the sun again.
Now, does the plant know where the sun shines from? On one hand, it doesn't have a brain, neurons, or anything like that - it doesn't "know" things in any way similar to what we call knowledge in humans. But, on the other hand: if you don't know where the sun shines from, you won't reliably move your leaves so that they face it.
David Chalmers defines quasi-belief in the following way (not an exact quote):
We can say an LLM has a quasi-belief if it is behaviorally interpretable as having a belief.
That is: you observe some behavior of an LLM. If you could say "Entity with a belief X would behave that way", then you can also say the LLM has a quasi-belief X. Or, when you see leaves rotating towards the sun, you can say the plant has a quasi-belief about the sun's direction.
Same goes for goals, or any other features we attribute to humans (including e.g. feelings).
(Note: this is very close to Daniel Dennett's intentional stance)
So, for example: Does ChatGPT have a belief that Paris is the capital of France? Well, it very clearly has at least a quasi-belief, as in many different contexts it behaves the way an entity believing Paris is the capital of France would behave.
Do LLMs have beliefs, or only quasi-beliefs? Do LLMs have goals, or only quasi-goals? Well, I think from the point of view of e.g. AI safety, these questions are just not interesting. What we care about is how the models behave, and whether they behave that way because they have "real" beliefs doesn't really matter.
This is not true for all attributes. For example, from the point of view of AI welfare, the question of whether models have feelings or quasi-feelings is fundamental.
So the TL;DR is that when people say "LLM believes X", they usually mean "LLM has a quasi-belief of X", and then they sometimes get pushback from people who assume this means full human-like beliefs. Note that this makes the same sense regardless of what we view as the difference between beliefs and quasi-beliefs.
Note that the usage of these terms and demand for rigor varies by orders of magnitude based on who you're talking with and what aspects of "belief" are salient to the question at hand. My friends and coworkers don't bat an eye at "Claude believes that Paris is the capital of France", or even "Claude thinks it's wasteful to spend money on 3p antivirus software".
Only when considering whether a given AI instance is a moral actor or moral patient does the ambiguity matter, and then we're really best off tabooing these words that imply high similarity to the way humans experience things.