Since cryptocurrencies do not really exist in any physical shape or form, they cannot technically be stored anywhere. Instead, there are private keys, which are utilized to access your public bitcoin address and transaction signatures - that is what you basically need to store. A combination of the recipient’s public key and your private key is what makes a transaction possible. There are several different forms of wallets, varying in terms of security, convenience and so fourth.
Changelly does not provide wallet addresses and never stores user deposits. To exchange cryptocurrencies on Changelly, you need to provide a previously-existing wallet address where you can receive your exchanged currency. Here is an overview of the best wallets in 2020.