What does that mean for you?
A wallet is a way to manage keys and payment information. Different wallets can manage different keys, while compatible arrangements may show access to the same keys on more than one device.
An address is also not the same as an entire wallet. A wallet can work with different receiving destinations without each destination being a separate software installation.
Can you picture an example?
Imagine you see the same spending access on a phone and another device. Deleting the phone display does not necessarily remove the other device's access. The record and the underlying keys matter more than the number of screens.
What should you remember?
Avoid assuming a new installation automatically creates an independent backup or separate ownership. Follow the relevant instructions and keep recovery information private. This is an explanation of the distinction, rather than a setup guide.