This will vary from one nation to another, but we can illustrate the types by examining the United States, and how there can be different territorial jurisdiction for different subjects: The Supreme Court of the United States has held that constitutional requirements of due process limit the exercise of subject or personal jurisdiction beyond territorial limits.
(Some states, such as California, have long-arm statutes that give their courts personal jurisdiction to the extent constitutionally permitted.)
In some exceptional circumstances, FRCP 4 grants a federal court personal jurisdiction when the law of the state in which it sits would not.
The leading Supreme Court stream of commerce case [1] resulted in a split, failing to clarify the issue.
Courts must decide in which locations, under what circumstances, the exercise of territorial jurisdiction over the citizen for claims arising from the website comports with traditional notions of fair play and substantial justice.