Everyone probably uses those terms slightly different and depending on whether it was a good sensation or not to them. What many call twitchy is just a change in the responsiveness from the deader handling bike they came from. And likely that would be something I'd describe as lively or sporty handling.
I just gave away last year my '91 Schwinn Paramount. It was a very nice ride, but very dead compared to the fun I'm having on the sportier handling Specialized Tarmac I now ride.
So those terms have to be looked at with a frame of reference of the one using them. Also, most people that say something is twitchy, will usually get used to it and probably months later describe that twitchiness differently or even not at all.