A disagreement is a semantic dispute if (1) the parties to the disagreement disagree about whether a particular claim is true, (2) they agree on all material facts, but (3) they disagree on the definitions of a word (or several words) essential to formulating the claim at issue (they have different understandings of the meaning of a word, the words are associated with different concepts). Consequently, their disagreeing on these definitions explains why there is a dispute at all; briefly, (2) and (3) together explain (1).
It is sometimes held that semantic disputes are not genuine disputes at all. But very often they are regarded as perfectly genuine, e.g., in philosophy. One might well wonder, of course, exactly what makes a Genuine dispute.
It is also sometimes held that, when a semantic dispute arises, the focus of the debate should switch from the original thesis to the meaning of the terms of which there are different definitions (understandings, concepts, etc.).
As a purely hypothetical example, one disputant, call him "Tim", might maintain that the United States has the highest standard of living in history. Suppose Joshua maintains the precise contradictory of that claim. Being reasonable people, they agree on all relevant statistical results, but they disagree about the meaning of "standard of living": Tim holds that "per capita income" is the meaning of (or at least an infallible or direct indicator of) "standard of living", while Joshua disagrees with this. In this case, Tim and Joshua have (suffer, are engaging in) a semantic dispute.