No, they are not. But if all he had was a deeply nasty personality, something he was born with, albeit modified via early childhood experiences and socialisation, then it is wrong to stigmatise those who are genuinely 'mentally ill' as somehow nasty characters, IMV.
Of course, this guy could well have been mentally ill and in great need of help. OTOH it might just have been an anti-social personality disorder that made him so abnormally aggressive.
Compare and contrast him with that guy who murdered two sisters in a park in Wembley. Police found he had been on the dark web dabbling in satanism and making pacts with some demon. Now that is the sort of thing that is classic schizophrenia, although I dare say he'll be treated by the courts as bad rather than mad. This guy responsible for the Keyham killings more closely resembles the far-right 'survivialists' one see in America, who see themselves as urban guerillas (Timothy McVeigh comes to mind). To me, the idea that being a virgin at 22 is a rational reason to do what he did strikes me as sociopathic rather than 'ill'. Of course, it is not possible to diagnose someone from a distance and his mother did beg for mental health support for him. Another possibility is some kind of genetic disorder - something wrong with his chromosomes that affects his wiring. I guess it is possible to be both mentally ill and have a personality disorder. Who knows? Just my 2p worth.