A character that an audience would rightly name as a villain has an objective within their narrative that is acknowledged by that character to be 'evil', or any other wording that acknowledges their motivations as the wrong thing. An example one may see of this would be the aptly named Dr. Evil from 'Austin Powers' (though a comedic example, he is a perfect one in this context). Even from his name, the audience knows that he does things because he knows it is the wrong thing to do, and for the express purpose of showing himself as evil, or for the personal pride of doing so. I would name this as a 'Villain by Nature'.
Of course, there is a another side to any coin, I would steer readers towards the villains of films who I would arguably not name as a 'true villain'. The opposite of this 'Villain by Nature' would be a type of character I would name as a 'Villain by Objection'. I would point out as a perfect example the primary antagonist of the video game 'Bioshock'- Andrew Ryan (It is no secret to those who know me that I could speak for hours on this character!). His objectives and ideologies go against those of the player, and the mentor watching over them- from this, it is clear the game has named and labelled him as the antagonist. However, the ideologies he announces and openly shows to the player are not evil- different, without a doubt, but in no way can the ideology be described as an evil act. The game pits the player against Andrew Ryan, and so the player immediately sees him as a villain. This is the reasoning behind a Villain of Objection- a character who has little to no evil acts associated with them, but is put against the protagonist, and so is immediately perceived as their opposite and inverse.
Think of 3 examples of villains from any media- are the a Villain by Nature, or a Villain of Objection?