ROM on android phones isn't really "read only"... right? I see the word ROM and internal memory used interchangeably in the context of Android phones. The OS seems to be stored in the internal memory itself, which is also used for installing applications. Which implies that it is not "read only".

So, just to clear my confusion, am I correct in understanding that in Android phones the OS is stored in the internal memory and word "ROM" is used for "historic" reasons, since ROM is where firmwares on non-Android phone were/are otherwise commonly installed?
It seems like you've been misinformed. ROM means Read-Only Memory and is used in Android as such.
The ROM is the part of your system that is: able to run on its own, write protected and thus not changeable.
Many/All manufacturers implement a way to bypass Linux' restrictions/file system permissions to be able to update their ROM ie. write to /system.
The normal user is not able to write to that /system partition, which is independent form the /data partition, where all your apps and data is stored (/data is not needed to run Android).
The only thing those two partitions share is (not always) the same hardware/memory chip.


  The contents stored on /system contain all software needed to run Android on that specific device including: drivers, configurations, scripts, applications, frameworks etc.
  They are read-only for the user and only writable after remounting as a system user or superuser/root.
  Therefore ROM can be considered a valid and correct term for the Android system's /system partition/ROM partition.