If this is a new occurrence (it did not happen in the past), the most likely cause is a dry drain trap in the downstairs bathroom. A drain trap is a double U shaped arrangement for the drain that allows water to be trapped in the U-shaped connection. The purpose is to form a water plug that prevents sewer gasses from escaping back through the drain hole. When this water evaporates, the gases can get through. You can see this arrangement if you can view the drain pipe under a sink. It is visible under most bathroom and kitchen sinks.
To solution to the problem is to dump water down the drain to fill the trap. This occurs most often in unused bathtub drains and floor drains. You may need to look under a floor rug to see if you have a floor drain. If you have a floor drain, just pour about a quart of water down the drain to fill the trap.
If this does not solve your problem, you may need to call a plumber to check out what is called the vent stack to see if that, or some other issue, is causing the problem.
Gravity. Also- If someone takes a shower with the curtain on the outside of the tub this can happen.
Same as upstairs BUT LESS drainage piping BUT more vent piping.
the pies are connected so when you turn on the shower the vaulve in the pipe going to the other shower might not be all the way closed thus causing it to leak
The drain is plugged somewhat between the upstairs and downstairs. Need to snake the drains.
The main drain is plugged. Not completely, but enough that it is easier for the upstairs water to come out in the shower and floor drain instead of going out the drain.
The drain from the toilet to the main drain is plugged and the branch to the shower is not. If the main floor toilet flushes, it is between the two toilets and not between the house and the sewer.
Sink, Taps, Shower, Radiators.
There is a main drain that runs from the basement through the roof where it is the vent for the system. If you look at the layout of the house, the upstairs bath is most likely over the downstairs one or the kitchen. If you look on the roof, you will see a 4 inch pipe coming through the roof that should be over the upstairs bath. The sink and shower drain into that and then to the basement and out of the house. Most likely the main stack is in the wall behind the toilet.
Take a shower, use the toilet
You have air in the system you need to bleed it out. do you have a really old heater/ boiler. hot water heater need more info
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.
There is a clog between the sink and the line to the street or septic tank. The sink is the easier path for the upstairs shower.