How do you check if a Character is walking?

I know that if you check a Humanoid's state you can see if a Character is Jumping or Falling, but when a Character is not moving it still counts them as Running/RunningNoPhysics.

BONUS QUESTION: What is the difference between Running and RunningNoPhysics?

Use the running event.

workspace.Player1.Humanoid.Running:connect(function(speed) --You can also do Humanoid.FreeFalling for falling and Humanoid.Jumping for jumping.
	if speed > 0 then --Walking
		print("Walking")
	elseif speed == 0 then --If speed is 0 then they've stopped walking.
		print("Stopped walking")
	end
end)

I saw your forum post: http://web.roblox.com/Forum/ShowPost.aspx?PostID=157922907. Humanoid.Running does work. Just check if the speed = 0. Running checks for the player's Torso's Velocity. If it's 0 they're not moving. If it's bigger than 0 they're walking.

Hope this helps!