How can I change the notification sound to a custom but non-default sound? Ok, so the title isn't as clear as it probably could be, but here goes:

In the Facebook Messenger application you can click the profile/settings button (top right on latest version) and there is a menu option for "Notifications &amp; Sounds".

In this sub-menu there is an option for "Notification Sound" which allows you to select the sound that will be played when you receive a new message.

This list appears to be a list of 'built-in sounds' with one exception... "Default ringtone (name of current SMS notificaiton sound)"

Basically what I am looking to do, is to change the notification sound to be different from my SMS message sound. (I actually used to have this working great somehow, but then my phone went for a repair and had factory reset).

The facebook app has a similar setting, but allows me to select from ALL my custom sounds. This is what I am hoping for.

Is it possible to get other sounds to be available in the list? How can I make it different from SMS notifications?

Samsung S7 Edge, Android 6.0.1
You'll have to add the desired tone to the /sdcard/Notifications directory (followed by a restart, possibly).

Alternately, you can install a file manager app such as ES File Explorer, which you can choose as the notification tone picker, instead of the default menu.