What does ';arising from same set of facts'; in a case means in U. S. Federal Court?

That's a fact specific determination. Here's one way to think about it. If you are telling the story of why there is one particular claim, have you essentially told the story of why there is another claim? If so, it's probably arising from the same set of facts. Note that that's just one way to think of it and won't necessarily always lead to the right conclusion. Also keep in mind that I am not a lawyer yet and this is simply an academic answer to an academic question, not legal advice.