As far as I know, the term “controller”, somewhat similar to a plug-in for the smartthings app, came into use with the V3 version of the smartthings app in 2018. At least that’s when it started to show up in the end user documentation.
I think the term may have come over from the old “Samsung connect“ app when that one was folded into the SmartThings app. 
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I run my account in a “hub optional“ configuration – – no hub at all. And my devices all still have controllers with version numbers. For example, I occasionally see the “update controller” message for my Meross devices, which are Wi-Fi and have a cloud to cloud integration.
Here’s another discussion thread showing the update message
Update Device Controller (New App V3)
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