Once we've worked through our fears about asking for what we want, a more precise language for asking for what we want is often helpful.
For example, there are often many things that we’re genuinely willing to do for a friend or a partner, even if it’s not something we intrinsically want for it’s own sake.
If you’re thirsty, I’m willing to get to get you a glass of water, happy to do so. I don’t desire to be giving you glasses of water for myself… if you’re not thirsty, I’m not saying, “please, would you take this glass of water, because I so enjoy carrying glasses of water over to you?” :D
And, the scope of things we’re willing to do or accept is typically broader than things we want for themselves.
Saying, “are you willing to do X?” is a very different question than, “do you want to do X?”
Another dimension is “do” vs. “try”.
The answer to the question “Do you want a massage?” might be, “I don’t know”. The answer to “Would you like to try a massage?” might be, “Sure, I’m willing to try it”.
“Do” suggests more of a commitment. If I ask, “do you want an hour long massage?”, that suggests figuring out ahead of time if you do want a massage for an hour… and perhaps I might be taken aback if after two minutes you leap up and say, “that’s enough!” But if the question is, “Would you like to try a massage”, that’s more open to the possibility that after two minutes you say, “no, this isn’t working for me”.
Combining both dimensions, “Are you willing to try X?” is a much lighter question than, “Do you want to do X?”
Here are are some examples of more precise phrasing:
A request (“May I…”, “Will you…”) is expressing the speaker’s want, and asking for the listeners willingness.
An offer (“Would you like…?”, “Do you want…?”) is expressing the speaker’s willingness and asking for the listener’s want.
An invitation (“I want this, do you also want it?”, “This would be fun for me, would it also be fun for you?”) is expressing the speaker’s want, and also asking for the listener’s want.
A statement of desire (“I want…”) is expressing the speaker’s want, without implying or asking about the listener’s want or willingness.
A inquiry about desire (“Do you want…?”, “Do you like…?”) is asking about the listener’s want, without speaking to the speaker’s want or willingness.
A demand expresses the speaker’s want, while saying “don’t care” to the listener’s want or willingness.
Since English is imprecise we can’t always unambiguously express a clear formulation in a simple sentence.
And “polite” requests and demands are often phrased like offers (“Would you like to pass me the salt?”)
So it can be hard to tell sometimes whether something phrased as an offer is actually an offer or not.
However we can ask for clarification! “Was that an offer or a request?”