Is there a word that describes when two or more people have different understandings of the same word?

I'm asking this out of personal curiosity, it's not required for a document or anything. My friends and I often have interesting conversations or debates, and often times we get stuck on an issue merely because we have different understandings of the same word. I use the word 'semantics' to try to describe it, but I'm sure that isn't the correct word.

My 'research' leads me to the word ambiguity, which I guess makes sense, but I'd like to know if there's a better word for it.

I am NOT asking for the word defining a word that has multiple meanings. (For example, wind meaning the gusts and to turn and/or crank a mechanism.) All other prior research leads to this answer.

Example for my question: If two people have the word 'justice', and each person knows the definition of the word, but take the meaning of the word differently, what is that called?

If my question doesn't meet some sort of preferred formatting, just tell me what I did wrong in posting this, and I'll rephrase it later.

A given individual's idiosyncratic use of language or words is called an idiolect, and a single word with multiple or ambiguous meanings can be described as multivalent but for generally describing the varying meanings of words, semantics is in fact correct. When you say "we are arguing semantics" you mean "we are arguing over the meanings/definitions of our words."

It's a little off topic for this SE, but it's worth mentioning that a number of noted philosophers have devoted their careers to semantics and the impact of semantics on philosophical debates.

Semantic discord

Semantic discord is the situation where two parties disagree on the definition of a word or several words essential to communicating or formulating any concept at issue.

Semantic disputes are arguments that arise over terms due to semantic discord.

A semantic dispute is a disagreement that arises if the parties involved disagree about whether a particular claim is true, not because they disagree on material facts, but rather because they disagree on the definitions of a word (or several words) essential to formulating the claim at issue.

Semantic disputes can result in the logical fallacy of equivocation.

Consider semantic dissonance.

dissonance: a conflict of people's opinions or actions or characters.

"I disagree with the first sentence but I suspect my disagreement stems from a semantic dissonance with the author."

If two people have the word ‘justice’, and each person knows the definition of the word, but take the meaning of the word differently, what is that called?

If two people are having a debate and are disagreeing with each other due to a fundamental misunderstanding of what the other person is talking about (as might be caused by their using different definitions of the same terms), this might be called speaking (or arguing) at cross-purposes.

Collins gives:

to be at cross-purposes with [somebody] to have a mutual lack of understanding with someone