In Pegging
Exchange Rate of a currency is tied to some other currency or group of currency
Example
Saudi Arabia has pegged its currency Riyal to Dollar since 2003
Peg Rate is 3.75
It means
1 Riyal = 3.75 Dollar
In Parity Value
Exchange Rate of a currency is fixed to an equal value of some commodity
Example
Price of gold in terms of rupee fixed at Rs 4800 /gram
Price of gold in terms of dolar fixed at $ 60/gram
Hence, Equivalent Price of USA Dollar against rupee= 4800/60 = Rs 80/Dollar