Is the notion of wanting or not wanting something well-defined? What is it?

[Sicnoo0]

There are a few things that I can reasonably surmise we do not mean when we say we want something.

1. We don't mean that it's in our best interest. It makes perfect sense to speak of someone wanting to sacrifice their wellbeing. A person who volunteered to go through hours of torture to save somebody else could claim that they were doing what they wanted to be doing for the entire duration of the torture.

2. We don't mean that we'd choose it in the event that it's on the table. Right now Alice does not want ice cream. However, if Bob were to offer her ice cream, Alice would choose to accept and eat the ice cream rather than not do so. The fact that Alice is inclined to accept an ice cream offer at any given time t doesn't mean she wanted ice cream at time t.

What does it mean to say Alice didn't want ice cream at time t?
What does it mean to say Alice didn't want ice cream across a duration of time T?
What does it mean to say Alice did want ice cream at time t?
What does it mean to say Alice did want ice cream across a duration of time T?

3. We don't mean that we approved of it happening to us. Alice gave Bob permission to subject her to a 10-second electric shock at intensity x. However, after five seconds of having endured the electric shock Alice begins to want it to be over. For those latter 5 seconds, Alice does not want to be subject to the 10-second electric shock that she agreed to. Nonetheless, she approves of what is happening to her for the entire duration of the shock.

Most people or animals with the capacity for understanding spoken language have developed an understanding as to how to act in response to someone expressing that they want something. Knowing how to act in response to what a person said is not the same as understanding the denotative meaning of what the person said. It's evident that using the word 'want' in conversation is perfectly functional when it comes to expressing a desire, because the other party will end up acting in such a way that aligns with how you would want them to act in response to your usage of the word.
I wonder if it would make sense to say that wanting has no denotative meaning but only a commonly shared connotative meaning.