なる(ことなる) The only verb of the bunch. To differ. と異なる: Use と when one thing is very specifically NOT like the other thing. に異なる: Use に when you want to say that something is different according to the circumstances (like xxxによって違う)
() Mathematical difference. Usually used in math, or the phrase 年の差が大きい!(the age difference between them is so big!)
(くいちがい) This is a BAD difference – a discrepancy or gap (i.e. a credibility gap).   $$$
(そうい) A more formal/newspaperish word for a difference between two or more things.
(かんかく) A distance or gap ;a literal space between two things:between two close-together buildings, say, or between the train and the platform.
(くべつ) To MAKE a difference or make a distinction between two things. (Opposite: 混同:こんどう: to confuse one thing with a similar thing)
(きょり) Physical distance between two things:towns on a map, for instance, or the distance between an archer and a target – a much bigger distance than the related word 間隔.