The shows have names and list of participants (what set of tokens you are trying to collect), everything else is left to the imagination. The game abstracts the shows enough that I wouldn't say they is a specific type or types of shows.
Given that you only have to retire one token after putting on a show, and it could be a potted plant, I consider them to all be dramatizations, and not actual fights to the death or anything.
I think the original version had one show that referenced Christians and Lions (albeit in Latin), but, given the above, I feel comfortable saying that no one gets actually fed to the lions, and maybe the Christians even win this one. (The show names may have been changed in the new edition, too.)