RG-58 is Coaxial cable. RG = Radio Guide. It is used for low-power signals and RF connections.
The 58 class has an outer diameter of 0.195 inches, 50 to 53.5 ohms impedance, and can handle up to 500 watts of HF (High Frequency) power.
RG58/U has a solid center conductor of 20 AWG bare copper. Its capacitance is 28.5 pF per foot.
RG58A/U has a center conductor of 20 AWG stranded tinned copper. Its capacitance is 30.8 pF per foot.
RG58C/U has a center conductor of 20 AWG stranded tinned copper. Its capacitance is 30.8 pF per foot. It's outer jacket is a different material than RG58A/U.
RG-58A/U or RG-58C/U was once widely used in "thin" Ethernet (10BASE2), for which it provides a maximum segment length of 185 meters. However, it has been almost completely replaced by twisted-pair cabling such as Cat 5, Cat 6, and similar cables in data networking applications.
RG-58 cable can be used for moderately high frequencies. Its signal attenuation depends on the frequency, e.g. from 10.8 dB per 100 m (3.3 dB per 100 feet) at 50 MHz to 70.5 dB per 100 m (21.5 dB per 100 feet) at 1 GHz.
I have no idea what R-58 A/JJ is. I'm only familiar with JJ as a designation for the BNC connectors on r58m like BNC-A-JJ (A JJ adapter).