By converting punched cards to 5-level paper tape you could send the data over ordinary telegraph circuits and equipment, including the Bell System TWX service. These circuits might be just wires, or telegraph carrier channels, or they might include regenerative repeaters for the 5-unit code. There were also private systems for transmitting 5-level code within a company or organization - these were supplied by Bell or by Western Union.
The Bell System didn't allow any "foreign" (meaning customer-provided equipment) attached to the switched network. They vigorously defended this position until it was overturned by the Carterfone case. If you wanted to use customer-provided equipment you had to lease a private line. You could lease a telegraph-grade line or a voice grade line which cost a lot more. So the IBM card-to-card transceiver came in a DC model that would work slowly over a telegraph line, and in an AC model that would work faster over a voice grade line. And since it did not need the entire bandwidth of a voice-grade line IBM designed the modem with four different frequency bands so that up to four systems could operate simultaneously over a voice-grade line.
The earliest modems were not really called that but were the carrier systems installed in telephone and telegraph company offices to allow multiple telegraph transmissions over a single voice-grade circuit. The cusotmer usually didn't know or care whether his leased line was wire from end to end or was transmitted over a telegraph carrier channel.
Modems, in the form of carrier channel terminals packaged to be self- contained, were sometimes used in manual TWX service to connect the teletypewriter on the customer's premises to the TWX central office.
In the late 1950s the Bell System deployed a message switching system for Delta Airlines. This used the voice telephone switched network to connect stations to each other. A cabinet of equipment about four feet high contained a model and an auto-dialer which went between the telephone line and the very complicated Teletype set used to transmit messages and dial numbers automatically. About the same time Bell provided a voice-grade private line and high speed (1200 baud) modems, called "digital subsets", to the FAA for transmitting weather data around the U.S. on a private leased voice grade line. Also at that time you could buy third-party modems operating to 2400 baud or so to use on private lines.
Then in the early 1960s the Bell System opened things up by leasing modems that allowed the customer to connect business machines to the modem and transmit data over the switched network. The EIA RS-232 standard interface soon followed. In the same time frame they converted TWX to a dial service, operating mostly over the voice switched network. Some other services were proposed, including a Wide Area Data Service, but these were shot down by the FCC. --
jhhaynes at earthlink dot net