The Turbotax Desktop program installed on your own computer from a CD or download can prepare more than one return, each return is a separate file, like having more than one word processing document on your computer.
Using Turbotax Online, each tax return requires a separate account with a different user name and password. (They can be linked to the same recovery email address if you like.). Each account will incur separate fees unless you qualify to file for free.
The smartphone "app" is a portal to Turbotax online. You would need separate accounts online for separate returns. I don't think you can download the app twice, you may need to log out and log back in under the other name to switch accounts.
