I read a lot of the original Hellblazer comics. The most definitive story for me... was when John Constantine was in a laundromat, and these strange paranormal-esque occurrences kept happening and these old women were talking about a mysterious figure about to arrive... so John Constantine just leaves. That to me is Constantine.
John Constantine is not a superhero, he's not even really a hero or anti-hero. He's just a guy.
Later interpretations really go all out with his magic. But if you read those original Hellblazer comics... he does an exorcism every now and then... but he uses magic extremely extremely sparingly.
He gets his ass kicked constantly. He relies on his best friend to save him from fights involving regular everyday humans.
When I see Keanu Reeves shooting demons or Matt Ryan sword-fighting the league of assassins, that's not Constantine.
My Constantine is a loser. A loser who has his moments. A man who hugged a lonely ghost. A man who cheered-up a Pagan God by getting him wasted. A man who gets his ass beaten by a rando on the street. A man who's ingenious plan to prevent his soul from being taken... is to just keep selling his soul to multiple demons. A man who had a heartwarming, loving relationship with his niece Gemma and pseudo-adopted daughter Mercury. A man who could not stop the nuking of an entire town, and became a helpless witness to an atrocity. A man who lives his life with self-doubt and self-pity, as he sees more and more ghosts of the people he failed. A man who is terrified of becoming a murderer, despite having done far worse to the people he called his "friends". A man who can't live with himself. A supposedly powerful magician who rarely uses magic. A lonely man. Who lives in crap apartments. A weak man. A man's who's birth meant the death of others. A man who is worn-down, tired, and sad. A loser.
That to me is Constantine.