I have a question with regards to how data is sent using single-wire cables between devices which are otherwise electrically isolated?
edit:
I understand now Coaxial has a common ground, but my question still stands: how is data transmitted without a common ground?
The real one wire transmission line is Goubau Line. See the patent:
https://patents.google.com/patent/US2685068
In the patent it's applied as low loss transmission way between microwave radio transmitter and its antenna:
Essentially the field between the mid wire and the shield of the coaxial cable is let to spread to fill the space. Only the mid wire is needed to guide the wave. At both ends there's a matching horn.
NOTE: there's no hidden second line such as the ground. The antenna tower can be any material.
Coaxial cable is two conductors sharing the same axis (hence 'coaxial'):
The shield carries the return current. If one or both ends has a transformer it need not be at ground.
Traditional telegraph wires used only a single wire, and the return current was carried through the ground.
These are both electric transmission methods- they work down to DC. There is only one way to transmit with no path for return current: using electromagnetic radiation.
COAX is, as others have already mentioned, is a two wire connection. So it sort of makes your question mute.
However, as long as the sender and the receiver have a connection to the planet as ground, you can indeed get away with a single wire, or even no-wire at all.
One way or another though, both sides need some form of reference point or differential measurement.
The most common way of doing this today is not using a copper wire, but an optical fibre. This eliminates the need for a common electrical potential (or the complementary signal on a differential pair) to refer the signal to.
A century ago, it was however common to send simple telegraph signals using only the local ground at each station as the reference. In practice, the necessary return current flowed through the ground, completing the circuit, but it meant that only one wire needed to be installed per signal channel.
This was particularly valuable for railway telegraphy, where there were typically three telegraph signals per pair of tracks plus a telephone connection - two block indicators and a signalling bell. This worked mainly because the telegraph was installed over a few miles at a time, so there wasn't much variation in ground potential.
Responding the the second half of the question, how to transmit without a common ground.
The easiest and most common technique currently used is differential signaling, avoiding a common ground is just one of the advantages.
Ethernet for example uses differential pairs. The ethernet cable, and a small portion of the device on each end has a floating ground. A transformer is then used to bridge the signals across the isolated domain.
Example circuit from https://www.audioasylum.com/messages/pcaudio/160168/ethernet-transformers-example-schematics-and-pictures
