Is there a specific distinguishing word for abbreviations that have evolved to be spoken words in their own right, like potus or Nato, sometimes even an "abbreviation word" with a clear meaning but without a definitive un-abbreviated phrase, like snafu? A collection of letters, in other words, that is no longer spoken as letters.
The term is acronym or word acronym. In a narrow sense, an acronym is differentiated from an initialism, which is pronounced letter by letter.
Merriam-Webster's Dictionary of English Usage (1994: 21):
A number of commentators (as Copperud 1970, Janis 1984, Howard 1984) believe that acronyms can be differentiated from other abbreviations in being pronounceable as words. Dictionaries, however, do not make this distinction because writers in general do not. [...]
Pyles & Algeo 1970 divide acronyms into "initialisms," which consists of initial letters pronounced with the letter names, and "word acronyms," which are pronounced as words. Initialism, an older word than acronym, seems to be too little known to the general public to serve as the customary term standing in contrast with acronym in a narrow sense.