Internet is not a network but a set of them. This set of networks provide connection between computers and equipments at a global level. Nowadays mostly all used networks are connected to internet or use the same technology. Why internet is the biggest and the only public network in the world? The simplest answer is all network technologies were designed to be small. Internet was born big and it was designed to be big. Of course some technology advances have been needed but no other network technology has become as big as internet. Once become a standard no other network technology can compete with Internet.
Fixed networks offer high-capacity connections but a reduced or no mobility to their subscribers. Access to fixed networks is provided always in the same building or area. Connection use to be a cable limiting mobility to the length of this cable. Thanks to the high-capacity and security of last Wifi standards every time they are more used for connecting to fixed networks instead of cables. In this case subscribers can move and connect anyplace inside the area covered by Wifi access points. Even in this case it cannot be considered mobile networks at all because this air connection is in charge of the customer.