Actually, that is not a gross oversimplification. According to [1], whether a crime has maximum sentence of over 1 year is precisely how the US government determines what crimes are and are not felonies:

In the United States, where the felony/misdemeanor distinction is still widely applied, the federal government defines a felony as a crime punishable by death or imprisonment in excess of one year. If punishable by exactly one year or less, it is classified as a misdemeanor. The classification is based upon a crime's potential sentence, so a crime remains classified as a felony even if a defendant receives a sentence of less than a year of incarceration.

Also, no, I wasn’t referring to post-release supervision (which is usually referred to as parole or supervised release). Many hundreds of thousands of people every year receive a sentence of probation for felonies, primarily because countless “tough on crime” measures have increased maximum sentences for minor crimes, which automatically turned them into felonies where they used to be misdemeanors.

[1] https://en.m.wikipedia.org/wiki/Felony