This is a good decade out of date, but there’s no real difference except that you can’t sign yourself out if you’re involuntary. They watch you a bit closer if your involuntary but otherwise treatment is the same. I once was give the choice and choose to go voluntarily because I figured I could sign myself out the following day. But that didn’t work, they made me involuntary and I was so mad I threw a fit. I was placed into solitary for my safety. It wasn’t being involuntary that they reacted to, it was my behavior.