This is a common question, some of the inflatables are even for wet use, so what's the big deal if it rains right??
The most significant difference is a wet use bounce houses are methodically designed for water use - a hose connects to a sprinkler attachment that wets the slide and runs down into a pool area. When we setup wet rentals we also take into account drainage (if the pool area overflows or when drained where does that go?) Rain on the other hand blankets EVERYTHING!
The blower on wet use bounce houses are methodically placed away from water and CANNOT get wet, it is NOT water proof, it's more or less a giant hair dryer without the heating element, and although a bit lower risk the extension cords should be kept dry as well. Water and electricity DO NOT mix. The blower could be damaged/broken and may hold you the renter responsible for replacement (~$200 for a blower) and safety wise it could pose a shock and/or fire hazard. DO NOT use the blower in rain or lightning! The expectation is that the blower gets disconnected and stored in a dry place should it rain/storm, once the rain/storms pass it can be reconnected again and used safely. THE RENTER is responsible for the equipment and the safety of all participants while being rented.
General Safety: Once a bounce house gets wet it is slippery, bounce houses NOT designed for water use also don't drain very well it'll puddle/pool in there. There are also insurance implications to consider since we rent these as a business, these are more or less pool rules - DO NOT use a bounce house when it is raining, lightning, or winds over 20MPH. If the inflatable is wet and lightning strikes it can electrocute anyone on there. Lightning isn't predictable this is why places like water parks make everyone get out of water during storms even if its just raining. Likewise we cannot setup in stormy weather 1) the inflatable will be wet as soon as we set it up and 2) for our own safety.
Business considerations: It's also very challenging to roll up and transport bounce houses that are soaking wet, ESPECIALLY the ones that are not for water use and it can take considerable time to dry them especially when water gets all inside the inflatables (I'm talking like where the air goes through inside inside where it is hard to get it out...) - same thing as rain vs. water use there is a huge difference in draining a pool, having a bit of water here and there elsewhere vs. having a 350lb inflatable covered in about 3 inches of water. Once we do get it back here we have to blow it up and let it dry out for several days (also weather permitting!), it cannot have any water left in/on the inflatable or it'll get moldy mildewy nasty!
Indoor setups: We can setup indoors, we've done several events in church/school gymnasiums, party rooms, garages, etc. that mitigates most all weather issues.