Communications satellites are not an extension of the earth's global IP network. The majority of communications satellites today send and receive frequency modulated (FM) digital signals.
FM is chosen over other modulation schemes for its unique ability to tolerate amplitude distortions and phase dispersions. FM better tolerates spectral intermodulations so the satellite-based power amplifiers can be biased lower to use less solar power for the same radio wave transmit power. FM also allows receivers to achieve signal-to-noise ratios better than carrier-to-noise ratios.
In digital FM, the streams of digital bits are divided into small groups of few bits. Each group of bits of a given bit pattern, called a symbol, is mapped to a unique radio frequency within the transmit band of contiguous carrier frequencies. The carrier frequencies are in the GHz range.
The sending earth stations use highly focused antennae to beam those FM radio waves to the geosynchronous communications satellites. The satellites act like bent-pipes to bend the radio wave beams back to the receiving earth stations.
The earth stations also beam FM streams of control commands, users authentication data, and software-download sequences to the satellites.
In addition to communications satellites there are many other types of satellites: military uses, GPS, weather forecasts, radio and TV broadcast, mobile phones, etc...