Goal: understand the single most important distinction in Bitcoin: owning keys vs trusting a company.
A wallet is where you hold your Bitcoin keys. An exchange is a company that can hold Bitcoin for you. If the exchange holds it, you’re trusting them to give it back when you ask.
Exchanges are great for buying/selling, but they are custodians. That means they control the private keys and you have an account balance— essentially an IOU. Wallets let you control the keys directly, which removes counterparty risk but adds responsibility.
Bitcoin ownership is defined by the ability to produce valid signatures under the relevant script conditions. Exchanges pool funds, manage internal ledgers, and net settle withdrawals on-chain. Your “balance” is not a UTXO you control.