Actually, juries are guaranteed unless waived for all criminal trials by the 6th Amendment and guaranteed on request by the 7th Amendment for any civil case where at least $20 is in dispute (which back then was a decent amount of dosh).
Thankfully, since you have to actually ASK for a jury in civil matters, they usually don't push it for most matters less than $5000 (depends on the state). In return for dispensing with the jury, we use small claims courts where the judge hears both sides, asks questions, and then decides the matter pretty quickly, saving some headaches all around.
And under most American laws, we do differentiate between felonies and misdemeanors, though not by the English standard. In America, a felony is a crime where there is a certain minimum standard of punishment involved (permanent record, loss of voting privileges, minimum 1 year sentence in a proper prison instead of a jail, etc.). It's our way to informing the perp, "You REALLY messed up this time.". Misdemeanors in our book are simply those crimes that aren't serious enough to be considered felonies.