There's at least a possibility that "suffering" is almost as specific.
Why? I'd expect that having a particular feeling when you're damaging yourself and not liking that feeling would be extremely widespread. (Unless by "suffering" you mean something else than ‘nociception’, in which case can you elaborate?)
I mean something morally meaningful. I don't think a chess computer suffers when it loses a game, no matter how sophisticated. I expect that self-driving cars are programmed to try to avoid accidents even when other drivers drive badly, but I don't think they suffer if you crash into them.
Thagard (2012) contains a nicely compact passage on thought experiments: