As a former railroad telegrapher from 45 years ago, I can give you some ideas about how it worked. Most railroads had relay offices located at division points. Individual stations on that division would send their messages to the divisional relay office and that office would then forward the message to the appropriate relay office for the message recipient. You weren't actually sending the message over a real long distance. These relay offices were full of special equipment. Western Union telegraphs worked on a similar basis. Most relay offices had the ability to cut the morse messages onto a paper tape for retransmission. The paper tape could be read by a teletype machine to create a hardcopy print. We weren't dealing with graphics or anything particularly high tech here! Early computer transmissions used the same type of equipment.

Morse telegraphy didn't require a real high quality signal quality to work effectively and many was the time when the voice lines would be unusable due to weather while the morse lines continued to work perfectly.

I seem to recall that the actual voltage on the line was higher than what was fed to the key and the sounder in the office. There was a relay unit that I recall lowered the line voltage to the 12 volts??? that went to the key and the sounder.

Railroad morse, known as the AMERICAN morse code, was really a timing of the clicking sound made by the sounder. A short click was a "dot" and a longer click was a "dash". The letters and numbers of the alphabet were represented by unique combinations of these dots and dashes.

Radio code, known as the INTERNATIONAL morse, is actually tones transmitted via radio. The codes used to represent the letters and numbers are about 50% different from railroad morse code.

A google search on "railroad morse" brought up 528 hits for me. Here are three:
American Morse Code
Innovators - Samuel Morse
Morse Code - History and Use