To be fair, describing Shadows and Personas as demons is accurate to the greater SMT lore. There may be some fine metaphysical distinction, but demons are also created through human belief and emotions. Persona 5 blurs the line even further by having the Shadows you fight literally be the same as the Personas you can recruit, which are the same models (usually) as the demons in the rest of the SMT series. Persona 1 and 2 establish that Personas are effective against demons, which are generally immune to conventional weaponry in the broader series and can only be harmed by other demons (or demon summoners, who usually have to have some sort of magic thingy to accomplish that). If they aren't identical, they are certainly cousins.

A big message in Persona 5 especially is that belief makes things more real, and conversely disbelief makes things less real. Your weapons, particularly the model guns you use, are props and escalate in power the more realistic they are, and in the Metaverse function like real guns firing bullets. On the other hand, being totally forgotten by everyone causes people to slowly cease to exist - in the real world, even.