In the US:
Officially Juvenile has only one program -- the freeskate.
Many juvenile skaters who are serious about training to compete at higher levels in the future like to "skate up" one level at nonqualifying competitions to enter the Intermediate short program to get more competitive experience in general and specifically experience skating a short program. If they're also serious about competing at juvenile level at regionals, they'll enter the juvenile freeskate at the same nonqual competitions where they enter intermediate short program. When they go to regionals as juveniles, though, they would only be able to enter the juvenile event, which is freeskate only -- same if they qualify to move on to sectionals or nationals.
Some nonqualifying competitions have noted the popularity of juveniles skating up to skate intermediate short programs at club competitions and have chosen to offer a separate unofficial short program event type just for juveniles. I can think of a few main reasons why a club might choose to do that:
1) A large competition might want separate the juveniles skating short programs from the true intermediates so that each test level gets a truer sense of where they stand against the skaters they'll be facing at regionals.
2) Especially if there will be events taking place simultaneously on more than one ice surface, it's easier for the referee to schedule the juvenile and intermediate freeskates, and final rounds if applicable, if they don't have to worry about time conflicts for individual skaters who might be entered in SP and FS at different levels.
3) Parents of pretty-good intermediates running the competition might want to help their daughters' chances of qualifying for an intermediate SP final round by not having them up against the best juveniles in addition to the best intermediates.
4) Designating a special juvenile SP event allows prejuvenile skaters, or hopeful juveniles-to-be this season who have not yet passed the juvenile test, to enter a short program event.
There are no standard rules for juvenile short program in the USFS rulebook, because it doesn't exist in USFS qualifying competitions. But clubs are allowed to offer nonstandard events in nonqualifying competitions if they make the rules clear in the competition announcement. If they offer a juvenile short program, the rules would probably be the same as intermediate short program with the exception that triple jumps would not be allowed.