What is the difference between (OH)2 and O2H2?

(OH)2 is 2 OH species, meaning two hydroxy molecules attached to a molecule. e.g- Ca(OH)2 which means Ca is attached to 2 OH moieties. Two separate molecules of linear OH are present. 
O2H2 is a peroxide molecule having a non linear symmetry. It is a stable having all 4 atoms bound together. 

 

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