Appointed would be the Government's choice. Retained will be supposedly your choice, but I doubt you can hire any lawyer of your choice since government can obstruct you and you'll default into hiring the lawyer of the government's choice anyway. I am talking about plaintiff's lawyer since I have no use for defense lawyer.
In a criminal prosecution, the plaintiff is the prosecutor. If you are being charged, you need a defense lawyer. Just about any lawyer can volunteer to get on the appointments list to be appointed as a defense lawyer in criminal cases, and a clerk normally assigns the cases in order, going down the list of cases and the list of attorneys. Therefore, it is very rare for an actual government employee to decide on a particular attorney for you. Typically, you get luck of the draw with appointments, whereas with a retained attorney you can pick your own attorney. I have NEVER been induced to get off of a retained criminal case by government pressure, so I question whether your fear of that is justified.
There are many attorneys, including myself, who will fight vigorously and imaginatively for the client that hires us. However, that does not guarantee victory, because if it did guarantee victory, no one would ever get convicted of anything.