I think the OP is talking about input/output impedances of amplifiers/guitar pickups, while you're talking about transmission line characteristic impedance.
Impedance of a transmission line is weird: in some ways, it acts exactly like a resistor, and in some ways it doesn't.
In contrast to a resistor, an ideal transmission line doesn't convert electrical energy to heat. Ideally, 100% of electrical energy put in one end of the line will make it to the other end of the line intact.
However, just like an ideal resistor, an ideal transmission line will have a real-valued impedance, not a capacitive (negative imaginary values) or inductive (positive imaginary values) impedance; nor will an ideal transmission line have any frequency dependence in its impedance: 50 ohms is 50 ohms.
One way I like to think of characteristic impedance is that it's the temporary impedance a change in signal will see until current/voltage wave reflections make it back from the other end:
For a 50-ohm ideal transmission line one light-second long (pretending we have velocity factor 1.0 to make the math easy), your ohmmeter would read 50 ohms for two seconds, and after that it would read whatever resistance is connected to the other end. If the other end is an open circuit, the ohmmeter would measure 50 ohms then infinite resistance; if the other end is a short circuit, the ohmmeter would see 50 ohms then 0 ohms; if the other end is terminated with a 50-ohm resistor, the ohmmeter would measure 50 ohms indefinitely.
If you have an infinitely long ideal transmission line with 50 ohm impedance, and hooked up an ohmmeter to it, it would measure 50 ohms. If you hooked up an LCR meter, it would show 0 impedance and 0 capacitance.
This indistinguishability between an infinitely long transmission line and a resistor is why a matched termination resistor prevents signal reflections: If you have some finite length of transmission line, and you attach either a matched resistor or an infinitely long transmission line with the same impedance to the end, the first length of transmission line cannot tell which you have attached - its behavior will be the same in either case: all the energy is passed into the next section.
Impedance of a transmission line is weird: in some ways, it acts exactly like a resistor, and in some ways it doesn't.
In contrast to a resistor, an ideal transmission line doesn't convert electrical energy to heat. Ideally, 100% of electrical energy put in one end of the line will make it to the other end of the line intact.
However, just like an ideal resistor, an ideal transmission line will have a real-valued impedance, not a capacitive (negative imaginary values) or inductive (positive imaginary values) impedance; nor will an ideal transmission line have any frequency dependence in its impedance: 50 ohms is 50 ohms.
One way I like to think of characteristic impedance is that it's the temporary impedance a change in signal will see until current/voltage wave reflections make it back from the other end:
For a 50-ohm ideal transmission line one light-second long (pretending we have velocity factor 1.0 to make the math easy), your ohmmeter would read 50 ohms for two seconds, and after that it would read whatever resistance is connected to the other end. If the other end is an open circuit, the ohmmeter would measure 50 ohms then infinite resistance; if the other end is a short circuit, the ohmmeter would see 50 ohms then 0 ohms; if the other end is terminated with a 50-ohm resistor, the ohmmeter would measure 50 ohms indefinitely.
If you have an infinitely long ideal transmission line with 50 ohm impedance, and hooked up an ohmmeter to it, it would measure 50 ohms. If you hooked up an LCR meter, it would show 0 impedance and 0 capacitance.
This indistinguishability between an infinitely long transmission line and a resistor is why a matched termination resistor prevents signal reflections: If you have some finite length of transmission line, and you attach either a matched resistor or an infinitely long transmission line with the same impedance to the end, the first length of transmission line cannot tell which you have attached - its behavior will be the same in either case: all the energy is passed into the next section.