Flat feet, slightly everted suitable running shoes? What's the difference between a support system and a stable running shoe?

Choose a stable one. The inner brace that supports the running shoes is very hard. This kind of shoes is not recommended unless you have serious walking and running posture problems. Ordinary splayed feet and flat feet, wearing stable ones is enough. There is no difference between stable running shoes and supporting running shoes, except for some big brands, they are not supporting running shoes.