That acronym defines usage very well. The other acronyms are actually misnomers, since none of the others are read-only.
Your first statement is clearly not true - there is nothing in the acronym ROM that relates how it implements Read-Only Memory and there many methods to implement Read-Only Memory but it is still ROM.
I agree with your second point. Acronyms like EERROM are really confusing because EEPROM is not really Read-Only - except that it functions LIKE ROM within the computer architecture.