Well for anyone willing to actually learn: what is an anti-hero?
An anti-hero is a character with a grey morality, far from the whiteness we are used with heroes. An anti-hero is that character who does the right thing even if that paints him as evil. But what does this mean? What's its difference with a villain?
It's their intentions what makes the difference. Let's use an example from a character that was already named: Keyaru, from Redo of healer. Keyaru is a poor bastard that after suffering things we shall not repeat here, he finds himself back before his hell started. Then, he decides to start his vengeance on the people that hurt him that badly.
Until here everything is alright. Sure, they haven't done anything to him yet because of the time skip, but they will. And maybe he's not the first. Until right now, everything seems fine. Sure, he's full of rage and spite but we can all empathise with him, even if he's not a hero or an anti-hero. At this point, he's simply a main character.
And then, it happens: that one guy and his squad of knights go to his village, kill everyone and even rape his childhood friend, the only person in this world that gave him a little peace of mind. After that, on his own words, he tells the reader that if they wanted him to be a monster, they succeded. To this point onwards, he will cast aside any decency he had and will start using anyone. Lying, abusing trust, manipulation... There's that beast girl he didn't even know, yet he didn't waste a single minute before manipulating her. And this, wheter we like or not, is the mentality of a villain.
Same with Anakin Skywalker, whose obsesion with saving his wife overrun even HIS WIFE. He didn't even care about what she wanted anymore. And this, my friends, lead us to a perfect example of an actual anti-hero: Shadow the hedgehog.
Shadow is an artifical life form created to acompany Maria, the ill daughter of Doctor Eggman. He's also the definitive life form and his actual purpose is to investigate for a cure to her. In multiple occasions, he does questionable things, but he never, EVER, does anything that could disturbe the rest of the now late Maria. His intentions now are simply to live a life whithout regrets and watching the world Maria never could. He may have done questionable thins but he never crossed the line or disrespected Maria's memory. He even helped Sonic's group multiple times.
And here lies the actual difference between a villain and an anti-hero. Intentions, attitude towards life and actions. An anti-hero is simply a hero in the shadow, doing the things the hero can't but without crossing the line that will turn him into a villain. The villain, meanwhile, is too far gone to reach him. Thank you.