Automatic Routines has Then options to “Change Security Mode” and “Change this location mode.” Is there a functional difference in choosing one over the other? “Change Security Mode” adds a notification option, but that is available as an additional Then option.
I understood the use of Location Mode a couple of years ago but it seems redundant now.
You can have routines firing on both location and security modes so depending on the routines you have, you can choose to set the location or security mode for the other routines to fire based on these as a trigger.
Nothing has changed about the distinction between security mode and location mode since security mode was introduced years ago.
These are two different variables used for two different purposes. As it happens, they do Use some of the same names for their values, but that’s just because Samsung is always terrible at naming things. 
The following thread is old, so it does use some old examples from the classic app and it refers to scenes, and SHM instead of STHM, but the examples have cleared up exactly this question for a lot of people, so hopefully it will help.
FAQ Routine, routines: How do you use them? (SmartThings Classic)
A Location Mode is a simple API object identified with a UUID that has a fixed name and editable label. By default there are three named and labelled as home, away and night but they can be edited so that, for example, the one named home has the label night.
One of the objects is defined as the ‘current’ mode. When testing the value of the Location Mode you are actually comparing UUIDs not strings under the bonnet.
You can create more Location Modes if you want, call them what you want, and assign any meaning you want to them. They have no default function associated with them, though they might be used in sample automations that are offered to you.
There is a very similar locationMode capability for devices but there never seemed to be any link to the Location Mode and it is now deprecated (but then so is bridge, which is now appearing more than ever, and so is execute).
Security Mode is tied in closely with the SmartThings Home Monitor app (STHM). Indeed when I once deleted the Home Monitor in my sleep the Security Mode also completely disappeared. Hopefully they fixed that.
The Home, Armed (Home) and Armed (Away) values of the Security Mode have defined meanings in STHM.
There is also something of a convention that the three values tie up with home, night and away in the Location Modes but that is all it is.
The Security Mode ties in closely with the securitySystem capability for devices. If you set the Security Mode you also call an enum command to set the securitySystemStatus attribute on every device in the Location with that capability (though I find it can be a bit hit and miss when automated). Similarly if you set the securitySystemStatus attribute on a device it will result in the Security Mode being set too.
Well, now I know! This community is priceless. Thank you all!
