How can an applicant know if his/her case is suspended? Is this something posted on online status checker? What is the difference between the cases that are waiting for security clearances for a long time and those that you mentioned are "on-hold"?
How do you know is a good question. Reports from applicants with suspended applications are very rare. I do not know.
That said, there is NO REASON to suspect an application has been suspended UNLESS the applicant knows of a reason. This is NOT something applicants need to worry about . . . UNLESS they already know there is something to worry about.
The one report here is contrary to that, I realize. I cannot explain it. But again, reports of this are so rare it is clear this sort of thing rarely happens to anyone who would not at least half-expect it is coming. So worry more about being struck by lightning than this . . . again, unless you know there is a reason to worry.
This is NOTHING like an application waiting on something like a routine update for a clearance. See the PDI previously linked for what applications can be suspended for. As noted, these are SERIOUS. Like an inadmissibility proceeding pending due to allegations of previous war crimes or involvement in a terrorist organization, or a very substantial misrepresentation, or being a member of organized crime.
Reminder: applicants generally have no reason to worry about delays in their timeline unless and until it approaches being a YEAR or so since applying. There is way too much impatient and unrealistic expectations in this forum.