"All-In-One"'s subdivide into "3-In-One" and "4-In-One".
My "3-In-One" type from Canon has a color scanner and an inkjet color printer, so it also has enough smarts to acts as a copier. However, it does NOT have the fourth element, a FAX modem. So by itself, it cannot send or receive FAXes, which meets my needs. I expected to do FAXing rarely, and NEVER expected to be receiving a FAX when I'm not there. So, I put a FAX modem into my computer. If I want to send a FAX of a printed piece of paper I can scan the doc into the computer, then "print" it to the FAX system which then asks me to specify what number to use, etc. And then it sends the FAX out using the FAX modem. Or, if the original material is an electronic file anyway, I can "print" that directly as a FAX without printing and re-scanning. If I want to receive a FAX, first I have to turn on my computer's FAX receiving software. Then the FAX modem can answer the incoming call. (It shares a phone line, so I have to not answer the call on the phone.)
A true "4-In-One" system puts the FAX modem into the printer. It can act as a stand-alone unattended FAX machine as well as a printer, scanner and copier. Usually it will come with software so that the computer can use it like a FAX modem, too. That is, you should be able to "print" any electronic file to the FAX sending system instead of the true printer if you want to.