One of my recent mediations boiled down to several issues, one of which was a warranty. One party (D) had requested a warranty, and was not provided with one. As a result, (D) felt that they had been disrespected and ignored. The other party (P) believed that they had done everything necessary and more, especially as the requested warranty was easily available on their website.
As it turns out, the parties were using the same name for two very different things. (P) understood the word "warranty" to be a guarantee that their product was free from major defects and could be returned if defective. The "warranty" (D) was requesting was an assurance that customer support would continue regardless of which representative they contacted for that support.
When involved in conflict, it is important to remember that we may not be using the same dictionary as the person on the other side of the table. While the meaning of a word or phrase may be obvious to one, it may not be to the other. This is especially true with "terms of art", words and phrases that have specific meanings in a trade or profession, but are used differently in everyday language.
So take a step back and make sure that you are working with the same vocabulary. Simplify that vocabulary if meanings are unclear, and do not hesitate to ask for clarification. This is not a sign of weakness; it is a sign that you are attempting to resolve the conflict in good faith. And sometimes clearer communication is all it takes to pave the way to resolution.