It does matter. When using the Online version all your tax information is stored on TurboTax servers. You can access your returns by signing into your online account with the exact userid and password you used to create the account.
When using the Desktop version, your information is only stored on the computer you used to create the return. It is not stored online so you cannot access it online. You can only access your return from the computer you used and the TurboTax software. You should not need to sign into the Desktop software unless you password protected your return.