A modem is a thing that allow your computer to connect with a network, such as the internet. It NEVER have any true sound capability. All modem don't have any kind of audio connector at all.
A modem may be in the form of an extension card that fit inside the computer. That was common with dialup modems, but it's getting really rare these days. Those where those that made that squaking sounds when connecting.
Normally, external modems are smallish boxes that stand between the computer and some data line, such as a telephone outlet or cable box. The connectors they have are : Power cord, phone or cable line and ethernet or USB cable going into the computer or router.
A desktop, or workstation, computer is a rather large box that get connected to the monitor, speakers, keyboard, mouse, modem, router, hub,... using a bunch of various cables. If you have a printer or scanner, those also connect to the computer.
A laptop computer have an integrated keyboard, a folding monitor and usually a trackpad. It also have some small speakers, often located in the same part as the monitor. It's usually possible to disable those integrated speakers. If there is anything connected into the audio jack, even partially, the integrated speakers get disconnected. If you forget your headphones connected, you get absolutely NO sound from the speakers.
Your computer does have some kind of sound card. It may be integrated into the motherboard or in the form of an extension card. Your speakers or head phones need to connect into it.
Most speakers are amplified. This mean that you must also plug them into an electrical outlet AND turn them ON, in addition to connecting them to the computer, to get any sound.
MOST monitors DON'T have any sound capability. Those that have are pretty rare. They are ONLY meant to display images, not play sounds.
Normally, you need to provide your own speakers.
They need to connect in the same connector as the one that you use for the headphones.