Isn’t that just another way of saying that there are "irreconcilable differences" in the marriage?

In one sense, yes, incompatibility and irreconcilable differences both mean that essentially the husband and the wife just don’t get along anymore. But in a legal sense, irreconcilable differences means that they cannot agree on certain fundamental issues and never will. Judges, satisfied with the claim itself, usually don’t ask what the irreconcilable differences are. In any given local court, a lawyer knows whether a given judge inquires about the particulars of irreconcilable differences. Most do not.

A classic irreconcilable difference is the complete failure to agree on how to raise any children of the marriage. Another classic irreconcilable difference is when one partner wants children and the other does not.