Generally speaking, there are two levels of crime in the US; misdemeanors and felonies. Both will land you with a criminal record, but a misdemeanor-only record will not show up on some standard background checks and does not remove your right to bear arms or vote, for example. Felonies are much more serious, and generally mandate a minimum prison sentence of 1 year unless plead down, while the sentencing for misdemeanors generally caps out at a year and typically just gets reduced to fines and community service, or a short stint (e.g. a couple weeks) in the local jail instead of a prison.

In some states, first offense non-violent felony convictions (e.g. exceeding the speed limit while fleeing police in a vehicle) can be expunged from your record when you turn 21 (if you were convicted and served out your sentence before turning 21). Otherwise felonies generally stay with you for life.

Unfortunately in the US we do in fact go so far as to criminalize urinating in public. It's weird to me that speeding (up to some limit) in a school zone is ranked below pissing in a shrub along the road.

Misdemeanors are actual crimes, yes.