Most road shoes have a two bolt pattern(MTB: ATAC, SPD, Ritchey, Egg beaters) in addition to the three bolt pattern(Look)and in some cases a four bolt pattern(Time, SpeedPlay).
So you can put a MTB cleat on most road shoes, but why would you, you end up with a shoe with no traction and a tiny cleat.
You cannot put a road cleat on a mountian shoe, wrong patterns, no room in the cleat box.
The advantages of road pedals are the large contact area, less chance of a hot spot, very good connection to the bike. Down side, hard to walk in and(except for SpeedPlays) entry is only on one side of the pedal.
With the mountian shoes you can walk around with out sliding, double sided entry, and they tend to be cheaper, shoes and pedals.
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I am in the woods and I have gone crazy.