A Repressive State Apparatus is when you are controlled through the fear of enforcement, which includes things such as the police, courts and prison. Althusser calls it repressive because the enforcement restrains the amount of freedom and choices that people can actually make within their lives. You don’t really have a choice that you can make when the threat of enforcement exists should you fail to comply with authority. An example of this would be someone seeing a sign on a bus that says “Assaulting MTA New York City Transit personnel is a felony punishable by up to 7 years in prison”. This person would then fear even the idea of attacking a MTA staff since they wouldn’t want to go to prison for 7 years.
The Ideological State Apparatuses are the natural thoughts and ideas that you are exposed to on a daily basis that you want to emulate in order to live a life that is deemed “normal”, which maintains the status quo. The way that it works is that multiple options are presented within many different aspects of life (politics, advertising, entertainment, etc) in order to give people the feeling that their choices matter and will greatly affect their position within their life, however, it turns out that these choices are simply an illusion that doesn’t change much within a person’s life within the grand scheme of things and ultimately keeps them within the status quo that has been established by the authority.
The difference between Ideological and Repressive State Apparatuses is that Ideological State Apparatuses are the ideas and thoughts within society that maintain status quo through people wanting to follow them naturally (since most people just want to live out their lives and feel “normal”) while the Repressive State Apparatuses are the fields of enforcement that come out when people aren’t following the status quo (while also being around to show to everyone what happens to those who do rebel against the authority).
The example that I have posted is a No Trespassing sign that mentions that those who do will be subjected to arrest. I feel that this is an example of a Repressive Ideological Apparatus, since it shows the threat of enforcement via the police should you not comply with the authority of that property.