A crypto wallet is often called a "bag for storing coins/tokens," but strictly speaking, it's software/hardware that manages the keys you need to control blockchain assets. The asset itself lives on the blockchain — the wallet is what uses your private key to sign transactions.
A wallet address is similar to a bank account number — it's fine to make it public. The private key/seed phrase, though, is the master key. If that leaks, someone else can move your assets.
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A wallet doesn't actually store the asset — it's a tool that stores and lets you use the key that gives you control over the asset.