The overlap between the two groups is so large and the justifications so similar that they may as well be the same. It is not useful for clarity, brevity or comprehension to distinguish the two.
"anti-vaxxer" is too broad of a term. That's like saying anyone who doesn't want to buy a Ford is "anti-car." They're not anti-car, they just don't want a Ford.
Almost all the people you call "anti-vaxxers", in fact very much believe vaccines are modern miracles that have reduced or eradicated serious illnesses. Many of them get a flu shot every single year. That's not the behavior of an "anti-vaxxer." "anti-vaxxer" is inaccurate at best, and intentionally derogatory at worst.
"THEY control us and manipulate everything, bruh! You're just a sheeple."
Baa, baa, baa! (Blowing rings of purple haze at you)
edit: btw. (·) https://en.wikipedia.org/wiki/The_True_Believer