Maybe they are multifocal glasses. This kind of glasses has couples of focal power on the lenses so the lenses are bigger than regular lenses. On the top of the lenses there is a pair of focal power which can help people to view the things in the distance clearly. While this pair of focal power is higher than our eyes so we can use them only when we put the glasses on the end of our nose.
Just depend on your reading needs. If you spend lomg time on reading, you may get full-sized lenses but you will find the distant objects blurry. If you look up from your reading frequently, you should wear your reading glasses on the end of their nose so that you can look over them at distant objects.
I know why they often wear reading glasses on the end of their nose. It is because they can see the things in the distance clearly so they don't need reading glasses when they are view things in the distance. Then they allow the glasses to slide to the end of their nose sometimes.