For the most part they are shoes that offer increased stability. For most people with foot problems, a stable shoe allows the foot to function in a more normal manner and helps the foot perform its natural job of absorbing shock. Of course, this is a generalized list and your needs may be somewhat different. Try the shoes on with the thickest socks you might wear with those shoes. Measurements should be taken while you are standing Have both feet measured.
Most people have one larger foot.
It doesn't matter that you wore a size 5 when you were 22 and the clerk is telling you to try a size 9. Only Cinderella always wears the same size shoe. Your foot size will change as you grow older. Also, sizes vary between brands. Don't buy a shoe if it feels too tight.