I've heard "Rails style" about as frequently as I've heard "Django style".

I've never heard "Sinatra style". In fact, when someone first mentioned Sinatra to me, they explained it as "like a web.py style microframework, for Ruby". This was a conversation between two Python developers though, so it makes sense we'd be more familiar with the Python ecosystem. But that's as much a Python-centric bias as your original comment seemed Ruby-centric bias.

Incidentally, I don't think Flask has all that much in common with Sinatra.