That's not the case in the US. Depending on corporate structure, if your business makes more revenue than expenses, even if none of it is paid out and it's all kept in the business, you will either owe corporate taxes on that amount (C-Corp or non-pass through LLC) or the full personal income tax rate (pass through LLC).
"Unrealized profit" is a term used for investments or assets afaik, when the paper value has increased but the gains haven't been realized by selling.
For a business, revenue minus expenses in a given accounting period is considered profit. The only question is whether it gets treated as corporate profit or personal income.
