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50 ohms: 50 ohms coaxial cable is very widely used with radio transmitter applications. It is used here because it matches nicely to many common transmitter antenna types, can quite easily handle high transmitter power and is traditionally used in this type of applications (transmitters are generally matched to 50 ohms impedance).
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75 ohms: The characteristic impedance 75 ohms is an international standard, based on optimizing the design of long distance coaxial cables. 75 ohms video cable is the coaxial cable type widely used in video, audio and telecommunications applications. Generally all baseband video applications that use coaxial cable (both analogue and digital) are matched for 75 ohm impedance cable. Also RF video signal systems like antenna signal distribution networks in houses and cable TV systems are built from 75 ohms coaxial cable (those applications use very low loss cable types).
You say the characteristic impedance of the coaxial cable. But I point to the impedance of PCB. E.g. the intermidiate matching between the two amplification stages. The microstrips of 50 ohm are usually used in the radio communication.
The attenuation of a coaxial cable is the lowest when impedance is about 77 ohm. Further a dipole antenna has a real impedance about 73 ohm. Therefore for CATV, where attenuation is important, a cable of 75 ohm seems a right choice.
Anyway, another important feature is the power handling capacity; it is possible to show that the maximum power trasmission in a coaxial cable is for an impedance of 30 ohm. A good compromise to obtain a good attenuation and a good power handling capacity is 50 ohm; this value is used for application where the power trasmission is important.
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