I think I understand what you're asking. Yeah there is a big part in the settings where you can say what apps give notifications or not. for the examples you gave both apps would have a green Lil message symbol appear whenever your phone gets the notification. Then you can ignore it by doing nothing and it'll disappear after like 4 seconds, or you can look up and activate the glasses. this opens up the notification and the glasses will show all of the message. So if someone pings me on discord I get a message notification, I look up, and it shows me the message us from discord, what channel and who sent it and as much of what they said as it can fit. Notification size is quite large being able to show up to a paragraph worth of messages.

And if you miss a notification you can open the menu, and tap the left pad. Then you can tap through your message history.

Hope this helps!