It’s unfortunately even more complicated than that, because the three things you see on the home screen for the SmartThings mobile app are in fact not “mode” but rather are smart home monitor “armed statuses.” Those are Arm Away/Arm Home/Disarm.
However, if you are talking about the home screen for your phone or tablet, not what you see after opening the SmartThings mobile app, then those are widgets and widgets are actually routines.
It’s extremely confusing because some of the smart home monitor support articles referred to “mode” for the armed status even though the term modes already existed for a different feature in the system. And routines are something different yet again.
The following might help:
So… If you’re referring to widgets, the widgets are related to routines. They have the same name as the routine they are associated with. You have to individually select which routine you want to appear as widgets on each of your phone/tablet devices. The most recent SmartThings mobile app update caused some problems with widgets and you might have to re-create them.
Also note that you have to do the selection step on each of your phone/tablet devices, so it is entirely possible that you could have different widgets on one family member’s phone than on another’s.
https://support.smartthings.com/hc/en-gb/articles/206145893-Is-there-a-SmartThings-widget-
SmartThings mobile app showing Smart Home Monitor Armed Statuses
SmartThings Widgets ( you select which routines show up as widgets for each phone/tablet)
on an iPhone
on an Android phone