Generally, AAMs are of two types, Ca-rich AAMs (alkali-activated GGBS) and Ca-deficient AAMs (MK or FA-based geopolymers). Considering this, is slag-based geopolymer a correct term?
"Slag-based geopolymers" is a correct locution, if the slag is used with other ingredients to obtain a geopolymer structure. Check the chapter 9 "Calcium based geopolymer (Ca, K, Na)-sialate, SI:Al=1, 2, 3" of "Geopolymer Chemistry & applications".
slag based geopolymer term doesn’t mean ONLY slag. As suggested by Frederic Davidovits, you have to know geopolymer chemistry to understand better. In GP reaction the precursor is the most important part of the binder, slag is very suitable but only if you know how to use. However in GP alkalis are used to generate new minerals like feldspars so in case of slag can be found anortite-like minerals. No efflorescence or leaching occur, even if put in water for long time.
While AAS means that slag is the main ingredient or even the only one used for the precursor part and needs to be activated with strong alkalis (super high pH, corrosive ambient) because it hasn’t the correct mineralogy/chemistry to work as geopolymer precursor alone. For AAM precursor isn’t well selected because the main “glue” of the system is the strong hydroxide, but this reaction isn’t closed. Alkalis remain soluble in water (leached out) or can migrate to surface reacting with CO2 (efflorescence).