These three terms tripped me up for the longest time! It doesn’t help that at the time Cornett developed Cued Speech, most professionals thought that speech was inextricably linked to language. So, Cornett called his system “Cued Speech”–even though the system doesn’t require voicing– and the name has stuck; but over time researchers developed newer, more precise terms.
Here’s the difference in a nutshell:
Cued Speech: the original name for the methodology as a whole.
Cued (American) English: the Cued adaptation for English, as used in the United States. The Cued British English variant has been adapted for different vowels according to UK pronunciation. You can also say Cued Spanish, Cued Mandarin, etc.
Cued Language: the newer name that specifically encompasses languages and de-emphasizes speech; it’s also the standard term used with disability accommodations– that is, Cued Language Transliterator, or CLT.