In the SmartThings context, “local control” usually means the ability to communicate with the switch without also having to go to the SmartThings cloud account. If you have a V2 hub, this is possible for some smart lighting automations, but only for some devices.
There’s no list anywhere of exactly which device type handlers can run locally. @SBDOBRESCU or @slagle may know which dimmer switches can.
Note that it’s not just the device that matters, but the specific device type handler you are using with it.
Insteon uses its own proprietary Communications protocol and does not integrate with SmartThings. There are some community members who have set up a separate device like a raspberry pi as a bridge, but this requires significant technical skill.
http://thingsthataresmart.wiki/index.php?title=Supported_Network_Protocols
As far as switches that look like the insteon switches…both insteon and Leviton dimmers use a Modified rocker form where you only press on the bottom of the switch. The Leviton is somewhat more pronounced, though. It’s on the official “works with smartthings” compatibility list, so you can see the pictures there.
https://www.smartthings.com/works-with-smartthings/-/filter/brands/leviton
Eaton makes the cooper aspire line in a unique style in several colors, including black. These are one of my personal favorites, they are also very well engineered.
If you use the stock device type handler it’s possible that the Coopers and
Levitons may run locally, but I remember there was something odd about which ones did and which ones didn’t. So hopefully someone else will have the specifics.
The new homeseer switches are traditional plain rockers, but have a number of unique features including the ability to process double tap and triple tap. However, they will definitely require the cloud to operate.
The following thread discusses the different features the different brands might have, so it might also be of interest. However it doesn’t discuss which ones can run without the cloud. But start around post 35 for the light switch discussion.