Yes. Internally, locally... What is the difference? The point is that the seed phrase and private keys are created, stored and accessible by your wallet software.
The slight difference is that on one end it is stored in their logs and any breach on their side can access it or the software themselves can easily steal your private keys and on the other hand it is not stored in their data logs but on the user's wallet file and not directly accessible to them.
There is always a risk when dealing with soft-wares even those that are open source, but is is much safer choosing one which is open source and reputable.
- Jay -