I read "custom ROM" and "customized firmware" all over the internet.
To my understanding ROM stands for Read Only Memory. Despite that I see links to files, that I suppose, are filesystem images, containing an operating system with preinstalled libraries and applications. What are these actually? Why do people refer to these as ROMs?
Also: cyanogen-mod's official description says: "[...] is [...] firmware distribution [...] increase [...] over Android-based ROMs [...] these versions of Android [...]". So they seem to use firmware, hardware component storing the firmware, and operating system interchageably. Do I see that right? Why is that?
Well, they refer to the firmware of the phone as ROM, because in theory you, as a normal user, can't alter the area where the firmware is (it's in the Read Only Memory). On older phone, this was true, it wasn't easy to alter a phone software without special equipment.
In nowadays, the firmware is not stored in real ROM, it's stored in the internal flash memory of the phone, which is not Read Only, so you can flash another firmware. As Farmor says, the 2 terms are interchangeable.
In general, people refer to modified firmwares as ROMs.