Value kept in PAI Up is always stored as PAI Coin. PAI Up uses an exchange rate to show you an estimate of how much your PAI Coin is worth in your local currency. When you send a transaction and enter the amount to send in your local currency, PAI Up uses the exchange rate to calculate how much PAI Coin to send.
It's possible people using other wallets are using different exchange rates, so the balance sent/received might be slightly different than what other person sees.
Since the exchange rate is always changing, the amount of value in your wallet as quoted in your local currency may change over time. However, your PAI Coin balance will not change unless you send or receive PAI Coin.