Aiding a crime is where you are committing the crime along with the other person and are helping them commit the crime.
So if you aid someone in a crime then you're just as guilty as that person who committed the crime and you can be charged the same.
When you abet someone in a crime you're not committing the same crime as them but you are enticing that person or encouraging that person to commit the crime.
Depending on the state laws and the crime that was committed you could also face the same charges as if you committed the crime.
For example if you enticed or abet someone in murdering someone then if the person is caught and you are caught you could both be charged with murder even though you didn't actually commit the murder yourself.