It used to be a lot simpler. The "Modem" received a stream of serial data (UART/RS232 + AT control codes).
The digital stream needed to be "encoded" and converted to electrical signals which could be sent on a physical wire.... most often the PSTN network (Public service telephone network)... aka "the phone line".
The audio/analoge technique used to produce the electrical signals was not as you might expect sending "blips" for 1s and silence for 0s. For way out of scope reasons that isn't efficient. Techniques like PCM or PWM, Pulse code/width modulation. Beyond the scope. However this gets you the "MODulator", "DEModulator". Which is you "MoDem"
Today, these still exist. Most would refer to them as "dial up modems". Rare. We tend to have "home broadband" technologies today which range from plain old twisted pair phone lines carrying 100s of times more bandwidth than an "analogu phone line", but over the same wires. We have old "Coax" cable for "Cable TV" carrying high speed internet. We even now have pure optical fibre connections in to the home.
At this point, really, it can be argued there is no modem. Certainly not in the terminology used to previously describe one. What often gets refered to as the "Modem" is usually an ONT or similar ePon/docsis device controlled by an ISP which "converts" or "bridges" the optical (or other broadband signal) to "Ethernet". Most, not all then additionally handle the authentication and "PPP" Peer to peer protocol used to transmit your data over this "You-ISP network". In larger enterprise these components can be broken down into individual (or multitudes of) different boxes. ONT, PPPoE client, Router, Firewall, Switch, Wifi Access point. In most homes they will either be a single box provided by the ISP or 2 boxes with one provided by the "Network operator" and the other by your "Internet retailer."
In 99% of cases, 10G makes no sense in home servers.
Because in 99% of cases "homes" typically have predominantly 1G networking and Wifi as the "Access network" with only a handful of users on it, usually not at the same time.
To upgrade this "1G" standard home network to anything faster will require the infrastructure be made available for higher speeds AND that the client devices are capable of taking advantage of it.
Concretely speaking, you will need to introduce a "switch" with higher speeds as well as upgrading the NIC in any currently 1G devices to the faster speed as well.
Practically and budget consciously, 2.5Gb is the present day sweet spot for consumer/pro-sumer "home" networking. It is relatively cheap, compared to 10G which "can" require a rewire if the CAT5e is substandard.
I have a single 10G link. It goes between two 1G + 2.5Gb switches. I used a simple "DAC" copper link between them.
I have 2 additional 10G ports, so I could link the two Proxmox servers which would take advantage of that speed during migrations and backups, but nothing else on the network is 10G capable or even close to needing to be 10G capable.
10G hardware typically costs a lot more to run. A 10G port might consume twice the power for the same data, even if it's never hit more than 900mbit/s.
Use-cases which could justify a house-wide 10G upgrade might be, video streaming. I don't mean playing a remote MP4 off the NAS via plex. I mean real time video streaming, such as lossless video conferencing, remote desktop with full 4K 60FPS playback capabilities. HDMI over Ethernet and so forth. Live uncompressed security camera footage etc. Remote gaming, ie. having a single beast of a gaming server with enough bandwidth to stream 2 clients at 60FPS. More bandwidth = less compression = less CPU = less packetisation delay = less latency = better gaming.