Either pot magnet or cup magnets it is named after its shape and they both refer to the same group of magnetic products. By gluing a round shape magnet into a steel pot/cup you get a prototype pot magnet and based on that prototype there are so many extensions being made by adding different accessories, using different shape components. Some of them could look so different from the prototype pot magnet but as far as their core working principle does not change, we still call them pot magnet. With the emerge of extension products other names are also used such as round base magnet, hook magnet, NdFeB pot magnet, flat pot magnet, ferrite pot magnet, pot magnetic assembly
The one concept that best describes rubber coated magnets or rubberised magnets is: it's a perfect combination of force and protection. Rubber covered magnets are actually one extension of pot magnet using the same working principle, but the rubber coating has greatly broadened the application scope of pot magnet.