Yes, the upstairs shower is leaking through the ceiling.
If the tub has a shower as well, the pipe from the faucet to the shower head could be leaking. You might also check the tube that comes OUT and fills the tub. It could be leaking back at the valve when you turn on the water.
A drain leak, a leaking shower pan, a leaking shower valve or piping, a leaking bezel or escutchions on the shower valve, bad or missing grout, bad caulking in the corners of the wall, a leaking shower door, water spilled on the floor, or, a drain pipe leak. any one or combination of the listed problems can do it. Look things over take care of what you can see wrong before making a hole in the ceiling. If you think you have fixed the leak repaint the stained area but prime 1st with Kilz or Binz to cover the stain or it will reappear through the paint even if the leak has stopped. If the leak hasn't stopped from taking care of the things you could see then open up a hole to see where it is coming from.
Common signs of a leaking shower pan include water stains on the ceiling below the shower, musty odors, and loose tiles or grout. To repair a leaking shower pan, the tiles and grout may need to be removed, the pan inspected for damage, and then repaired or replaced as necessary.
Your bathroom ceiling may be leaking due to a plumbing issue, such as a leaky pipe or a damaged seal around the bathtub or shower. To fix it, you should first identify the source of the leak and repair it. This may involve fixing the plumbing, resealing the bathtub or shower, or replacing damaged ceiling materials. It is important to address the issue promptly to prevent further damage and mold growth.
There are several possibilities; some of them indicate plumbing problems, and some of them are just consequences of physics. If the ceiling in the room with the shower drips all over during a hot shower, it may simply be that water vapor from the hot water is condensing on the relatively cool ceiling and dripping. If the ceiling in the room with the shower drips in a particular place, then it may be that the hot water pipe is leaking. (It's unusual for the hot water pipe to run through the ceiling instead of running up inside the wall, but it's not impossible.) It's also possible that it's condensation again, but that the condensation is only occurring at a particularly cool spot... perhaps where the ventilation system or a cold water pipe runs through the ceiling above. If the ceiling in the room underneath the shower drips after someone takes a shower, but only a hot shower, again it's probably the hot water pipe. If the celing in the room underneath the shower drips regardless of whether hot or cold water is used, then it's most likely a drip in the shower drain pan.
Is your shower faucet leaking and needs fixing?
Shower body or pan not properly supported or the joint not properly caulked possibly a fiberglass pan with plastic piping
If it is indoors and not a recessed shower, you may have a leaking shower pan.
Common causes of a leaking shower include damaged grout or caulk, a faulty shower pan, or a worn-out shower valve. To fix a leaking shower, you can reseal the grout and caulk, repair or replace the shower pan, or replace the shower valve if necessary.
The Bobrick shower curtain cannot be installed in the ceiling. It is made be installed in the shower wall brackets.
If your shower pipe is leaking, it may need immediate repair.
Is your shower drain leaking and causing water damage in your bathroom?