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That would be $0.03 profit, right? Is there something wrong with this logic and is there anything I need to know?

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Correct would be: You buy coin/BTC for 1$ and sell coin/BTC for $1.03 (both on Binance) later... Then the profit is $0.03.

If you sell the Ether for $1.03, the profit of it is dependent from the price you paid for it earlier. Did you pay $0.80? Then the profit is $0.23.

And you can't know the profit of your BTC-trade because you'll sell it in the future.

Don't compare apples with pears (BTC with ETH).

And what you need to know: They could have trading fees

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