When you press F3, you can now see the difficulty but contrary to what is written, the difficulty is general (peaceful, easy, normal and hard) and not regional/local. Similarly, the day counter doesn't indicate the number of days spent in the same area. In this case, the "local" word is not necessary and the day counter doesn't need to be in brackets, since it doesn't relate to the difficulty.
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The local difficulty is a derivative of global difficulty settings and total world time, but it's still the local value that is displayed in the debug screen.
FYI
In 1.9.3, the debug screen shows values: x.xx // y.yy (Day zzzz)
In single-player, the values are correct (and y.yy is the final 0.0 - 1.0 local difficulty rating)
In multi-player, the InhabtedTime for each chunk is not sent in the packets from server to client, so the client always assumes the InhabitedTime of every chunk is 0, causing the F3 debug info to be under-valued on the F3 screen when connected to a server.
Please read http://minecraft.gamepedia.com/Difficulty (scroll down to "Regional difficulty") please, for understanding how it works
in English