In some states, minor traffic violations are considered "crimes." Other states classify minor traffic offenses as non-criminal civil offenses or infractions. But regardless of nomenclature, the court procedures for minor moving violations like speeding and stop sign tickets are almost always different than those for more serious criminal offenses.
For starters, traffic citations are generally handled in an entirely different court than other crimes. Most jurisdictions have traffic courts that are specifically dedicated to minor moving violations. These courts are generally less formal than criminal courts. And some of the rights that a criminal defendant would normally have—such the right to a jury trial and court-appointed counsel (though you can hire a private lawyer)—often don't apply in traffic court. The idea is that more relaxed standards can be used in traffic court because the consequences of a conviction aren't that severe—a convicted motorist is typically looking at just a fine and the DMV assessing traffic violation points.
With more serious driving-related offenses such as drunk driving, reckless driving, and vehicular homicide and manslaughter, there's more on the line for the accused driver: a conviction usually carries the possibility of jail or prison time. So, a motorist who's charged with one of these crimes will typically go to criminal court rather than traffic court. In criminal court, not only do things have a more formal feel, but the system is a lot more protective of the defendant's rights. Almost everyone is represented by an attorney. Defendants who can't afford an attorney have a right to court-appointed counsel. And, generally, defendants who want to fight the charges have the right to have a jury decide their case. To get a conviction in criminal court, the prosecution must prove the defendant's guilt beyond a reasonable doubt. (Many states have a lesser standard of proof in traffic cases, making it easier for the government to get a conviction.)
Another major difference between traffic violations and more serious criminal charges is what happens after a conviction. A criminal conviction is going on your criminal record. So, when employers or anyone else investigates, the conviction is generally going to show up. (However, there are often ways to clean up a criminal record.) Minor traffic violations, on the other hand, don't go on your criminal record—just on your driving record. But remember, more serious driving-related offenses like DUIs are considered regular crimes, so they will affect your criminal record.