In this usage, only a tool that holds keys locally is a crypto “wallet” at all, and any other modifiers or caveats are suspect. In this schema, your crypto on Coinbase or Kraken isn’t in a wallet at all, just an account. Unfortunately, it may be too late to reclaim this rhetorical high ground after years of obfuscation by regulators and (to a lesser extent) exchanges.
Source: https://www.coindesk.com/layer2/2022/02/02/a-crypto-wallet-by-any-other-name/