Why would you expect that? If the purchasing power of that wage isn't the same, then it will feel different. If the only thing changing is the currency value, then sure, it will feel similar. Currency exchange rates != purchasing power.

The reason there's a difference between the two is that currency exchange rates are calculated using different inputs than purchasing power rates are. Purchasing power compares things like milk and eggs and gas whereas currency exchange is mostly limited to fairly liquid financial instruments like bank notes and bond instruments.