A violent crime is a crime in which someone uses force or injury (/possible death) to commit a crime. These are the type of crimes we would probably want to see as a "red flag" or a thing to make sure you look out for. Some people have different lives after prison and are better people, but violent crimes are important to both be wary of and make sure we never.  

Non-violent crimes include anything that does not include the injury of another person, or forcefulness of illegal action. This means drug possesion charges, alcohol crimes, underage drinking crimes, burglary, theft from stores, etc. A lot of these types of crimes are done out of desparity, or need for essential resources. 

Laws that apply in the state in question, each state has different statues and regulations that they abide by. There are even local laws that are different, so always make sure you are looking at what the laws are in your area before doing something that is ambigiously illegal. 

These are laws and rights that are enshrined in the Constitution and Amendments, our federal law outlines how many state laws are formed. This means that when in airports or on flights, you may be under different regulation than in your familiar area. 

Because there are state laws and federal laws, we also have state prisons and federal prisons. Typically the prison you live in correlates with the crime you commited. State prisons are typically for shorter sentences. State Prisons often have less protection or security than federal prisons. 

Federal Prisons are going to be mostly for federal crimes, or higher level/ violent crimes. The prison system in the United States, has very few regulations on labor and living areas of the people residing in the prison.