> Further, an ad hominem is when a person attacks someone's character without any base.

An Ad-Hominem is specifically an attack on someone's arguments using some un-related attack on their character.

EG: "Dr. John's Opinions about vaccines are invalid because he smokes cigarettes." or "James assertion that the earth is round is invalid because he thinks that dogs are better than cats."

Ad-Hom is short for argumentum ad hominem. If you aren't making an argument with your attack, you are just insulting someone.