I think in English there is also:

• Comparing the subject to an animal, such as a dog.
• Slurs for various minorities.
• Names for 'vulgar' body parts, or the act of sex itself.
• Names for human waste products.
• Literal 'curse words', such as "damn" or "hell", which imply the subject will go to, or just allude to the existence of, the Christian hell.
• Literal swears, as in oaths. This is pretty rare in modern English aside from "I swear to god... ". The word "gadzooks" is actually a minced version of "God's Hooks" (the nails used in the crucifixion), which was probably shortened from "I swear on God's Hooks". Its pretty funny how something that was probably deadly serious in the past has been diluted so much that now only cartoon characters say it.
• Literal profanity, as in invoking the holy in an improper context. This has a lot of overlap with the previous two categories.

I don't really know anything about linguistics, but these seem like the categories to me. In addition to the "alludes to the sexual impropriety of the subject (if female) or the subject's mother (if male)" category.

“Yer daddy was a 2 pump chump!”

Edit: Not sure how that comes back to “mom’s a whore”