A pretty big one was the Colombia University accusation.
Even before the investigation began, the charge had immediate consequences. Nungesser was placed on restricted access to university buildings other than his own dorm; these “interim measures” made it extremely difficult to continue in his campus job as an audiovisual technician (especially since he was not allowed to explain why he was under these restrictions) and to attend the counseling sessions he had started. Meanwhile, it became obvious that despite confidentiality rules, news of the accusation was spreading: Within a few days, Nungesser says he was being conspicuously shunned by many fellow students.
His name has been plastered on campus bathrooms and published in easily searchable articles. His face is visible online, too, in photos that detractors have posted as warnings to strangers.
http://www.thedailybeast.com/articles/2015/02/03/columbia-student-i-didn-t-rape-her.html
And if so, is it any different from media outlets doing that shaming to all sorts of people?
Absolutely. There is nothing quite like the accusation of rape in terms of how damaging just the accusation is. Maybe accusing someone of being a pedophile, but that is much less frequent. Being merely accused results in being ostracized by everyone. Your family, your friends, your classmates, even your job. People lose their careers due to false accusations because their employers don't want to deal with the potential for it being true.
They lose their families and everything they've worked for because some woman claimed she was raped. It doesn't even matter if it's true, just accusing someone is a social death sentence, if not an actual one.