There's 2 types of counter puncher, avoid and counter (Floyd Canelo etc) or punch when you punch (Inoue GGG etc)
I see what you mean but the punch when you punch style is also a form of countering because you're responding to an opponent that is instigating the move, so I still call that counter punching. But I agree its not pure counter punching as evading and countering, or catching and countering are
Nice not many people recognize that difference. It takes elite focus, timing and anticipation to successfully counterpunch in that way. Sergio folded Paul Williams with that style same as Juiced up JMM when he slept Manny.. Canelo recently used it effectively when he crushed BJS face..
As much as i don't like his diva tactics and the paid referee - Canelo. You got to handed to him. Absolutely monster in that department, and everything else. Just like always i try to be unbiased. The guy is a freak machine, and i'm saying freak machine and not freak of nature, cause he is busting his **** of with insane hard training, and he never stops even with all the money, fame and etc. he has earned through the years. I respect that. The next big name is Usyk. He is incredible counter-puncher. He feints and bait you, make you miss and punish you like no one else with incredible combination. But Usyk is way more than that. He obviously slowed down, as he is no longer in his prime(neither of his fights in the HW was in his prime). But in his prime in the CW he was a monster. Just look the matches against Huck and Gassiev, they are telling the whole story of what an incredible counter puncher Usyk is.