There are 2 ways for SmartThings to support a Wi-Fi smart device:
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Cloud to Cloud integration. Setup the device on the manufacturer’s supplied cloud platform, then link that cloud platform to SmartThings. From that point forward, you can control the device through either SmartThings or the device manufacturer’s app. You don’t need a hub for this. Examples - TP-Link Kasa Switches, Google Nest Thermostats, and many others.
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Local Wi-Fi integration. You’d need a hub for this. SmartThings doesn’t have many devices they control this way, but there are drivers from many folks in the community to control some of these types of devices. For example, devices flashed with Tasmota firmware. This driver supports 2000 different Tasmota-flashed devices:
It all depends on the devices you have; you’d have to provide the manufacturer and type of device to get specific advice on how to integrate each device.
In both cases, though, the Wi-Fi communications still go through your router. For local Wi-Fi integration, it’s just that the SmartThings hub will send commands to your devices, but still through your local router.