Criminal cases are when a law is broken. Therefore, jaywalking is indeed a criminal offense, albeit a very minor one.
As for speed limits and jaywalking specifically, you appear to be right that they aren't criminal offenses until a threshold has been crossed (e.g., speeding 15 over the limit). But those seem to be considered 'infractions', and I admittedly don't know where the lines are.
Felonies are major criminal offenses. Misdemeanors are minor criminal offenses. Infractions are oopsies.
Most traffic charges are treated as infractions, even when they lead to levels of damage or injury that would ordinarily mean a misdemeanor or felony. Cars are somehow "special." If you want to get away with murder in the US, definitely use a car not a gun.
(But don't be drunk. Drunk driving is no longer socially acceptable -- if you're drunk and kill someone with your car, that's serious jail time. If you're just a bad driver and kill someone with your car, that's an oopsie.)