OK, this actually got me when I first started in the blockchain space.
You don't really have a wallet. You have a secure crypto key that can access an address on the blockchain. That means your ETH and HST are always available using any method (MyEtherWallet or any other program/service) as long as you have the secure key you got when you created the address initially.
So - that means it's all about that key. You can have it as a hot wallet, which means you have it on your computer and it's convenient; but if your machine is hacked you are vulnerable. OR, you can take that key and store it offline - in cold storage. Either by moving your key to USB storage and putting it in a safe, or printing out that PDF and making a paper wallet and doing the same. That means its more inconvenient to use, but far safer.
The third option is buying a hardware key such as a Ledger Nano S. This means its still available to use on your computer, but you physically have to press a button for the key to work, so even if hacked you are safe.