Pedantry warning, but I think this distinction is useful: The phrase “civil crime” doesn’t really exist. You can have a crime, you can have a civil case, or you can have both; but they are separate things.
Criminal court is where the government prosecutes someone for allegedly breaking the law (committing a crime). A pardon wipes out the government-imposed consequences of that crime.
Civil court is for legal disputes between parties. It’s not about punishing crimes but about one party seeking restitution from another. Sometimes that stems from a crime, but the civil case stands on its own.
So even if a crime is pardoned, the door stays open for civil lawsuits over the same event. (This is repeating your point. My beef was just the “civil crimes” phrase!)