{complete} If the story's status is complete, what do you suppose that means? Yes, the story is complete. Finished. Done. Ka-put. The end.
{ongoing} Ongoing fanfics are still in the process of being completed. There may be one chapter or several, but it ain't over 'til it's over. Then it's moved to the "complete" status.
{on hiatus} If a story is on hiatus it is not finished, but the author is not working on it either. Sometimes people get busy. Sometimes we have more than one story that isn't finished and we have to quit working on one in order to finish the other. In these cases we put the story on hiatus and will get back to it eventually. Sometimes it only takes a week, sometimes it may take several months.
{offline} This is different from a hiatus. A story that's offline is usually a story that's been lost, either completely or in parts. Sometimes it's a story that's finished, but I can't put it up because I'm too busy to at the moment. These are usually up again long before hiatus stories are.