Online storage of cryptocurrency is the approach used by a hot wallet, the entry that covers it in detail. In crypto usage, "online storage" does not mean cloud file storage; it means keeping the private keys that control coins on a phone, computer or server connected to the internet.
Keys held online can sign transactions instantly, which is why exchanges keep a working balance this way to process withdrawals, and why everyday users choose mobile and browser wallets such as MetaMask for trading and payments. The cost of that convenience is exposure: anything reachable over a network can be targeted by malware, phishing or server breaches, and many large thefts from exchanges have involved hot systems.
Industry practice is to keep only the amount needed for day-to-day activity online and the rest in offline storage, also called cold storage. Exchanges and custodians often move funds between the two on a schedule. The pairing is sometimes described in banking terms as the difference between a till and a vault, and the wider choice of who holds the keys is covered under custodial vs non-custodial wallets.