Difference between requiring an encrypted device password pre-boot or post-boot?
If the phone boots up without asking for a password, it is most likely not protected by encryption in the way you would expect.

In theory, it might not be encrypted at all. But as you note, that's not plausible if you can change between the two options on the fly. More likely, it is encrypted with a default password, meaning that anyone accessing the phone's storage outside the normal UI login procedure (e.g. by flashing a custom encryption-aware recovery like TWRP or via ADB) can access your data. Your password is then only used to provide entry to the user interface – not protecting you from outside access to the phone's storage.

If you need to enter your password for bootup, it is that password that is (hopefully) used for encryption, meaning that outside attacks should only be possible by cracking your password (provided that Samsung's custom implementation is cryptographically sound). You can check that encryption is active by trying to mount your data partition in TWRP.

It is surprising that Samsung doesn't clarify the fundamental difference between the two options. But then, Google themselves are possibly even more careless in Android's default implementation as indicated in this blog post.

The author states that on enabling accessibility services, all you get is a cryptic message that "your device won't use your lock screen to enhance data encryption" before the encryption password is reset to the default password – effectively disabling encryption for all practical purposes and giving anyone with a bit of technical understanding full access to your data. The Android encryption documentation seems quite proud about the default password encryption being "resilient against off-box attacks", but attackers will likely not care as long as they can access your data "on-box", ie. with the storage installed in your phone.

Whether Samsung's implementation uses Android's default behaviour described above or a proprietary way of switching between encryption passwords, it is quite likely that only one of the two options provides any meaningful protection that goes beyond using a password on a non-encrypted phone.