What's "Forum Non Convenien"? And what's "Anti Suit Injunctions"?

Answer 1

Forum non conveniens is a grounds for dismissal, on motion, of a civil lawsuit. It means that the court in which the suit was brought has agreed with the defendant that
1) there is another court in which there is jurisdiction over the matter;
2) the parties are subject to the jurisdiction of that court;
3) the holding of a trial on the matter in the current court would present an overwhelming inconvenience to one side or the other; and
4) there is no other reason why the lawsuit should not be held in that court.

Anti Suit injunctions are different: they are a ruling by one court (#2) that the same parties already have another case over the same issues in another court (#1), and that, therefore, the second suit (and any others) should be enjoined - or stopped - because the first case will settle the issue.

Answer 2

Forum non convenien means that the court is not favorable to a party while anti-suit injunctions is an order of the court prohibiting an agency, institution or tribunal to perform a certain act that will jeopardize the rights of another person or entity.