Money kept in your BRD Tezos wallet is always stored as tez. The app uses an exchange rate to show you an estimate of how much your tez is worth in your local currency. When you send a transaction and enter the amount to send in your local currency, the app uses the exchange rate to calculate how much tez to send.

It's possible people using other wallets are using different exchange rates, so the balance sent/received might be slight different than what other person sees.

Since the exchange rate is always changing, the amount of money in your wallet as quoted in your local currency may change over time. However, your Tezos wallet balance will not change unless you send or receive tez.