In most of the US, "employment-at-will" eliminates the distinction. A company doesn't need to show a cause in order to fire someone. Where it becomes important is that if someone is fired "with cause," then they are not eligible for the company's typical severance benefits or unemployment compensation.
This, in turn, creates a perverse incentive for employers to fabricate a cause, or even to provoke the employee. Fortunately not at my present employer, but I have seen this happen and have also seen managers brag about it.
I've been laid off a couple times when the company I was working for shifted directions and my skill set no longer met their needs; with smaller/younger companies (especially in our industry) it's to be expected from time to time. To me, though, being fired is what happens when an employee fails to perform their job satisfactorily.