I believe the SmartThings presence sensor is a zigbee device, not zwave. The SmartThings hub can handle both zigbee and zwave protocols.
The ST presence sensor registers as “on” as soon as it is within range of the ST hub, typically about 50 feet. (The store description says “35 to 50 feet” but sometimes it’s a little further. It can get thrown off by all the usual things that can block zigbee signals.
The only reason you’d want to know that it’s zigbee, not Zwave, is if you want to put a repeater device in your garage or a street-facing room so you get a little further range. The most typical repeater people seem to use is the ST old motion detector, which can act as a zigbee repeater.
The mobile presence phone detection works using the GPS in your phone. Normally that triggers somewhat further away than the ST device, around 500 feet. However, geolocation services for cellphones are using range as well and your hub might get sent the location of the cell tower that found you (I don’t know if that’s always how that works), so you yourself could be in a slightly different location, a block or two nearer or farther.
If both your ST PRESENCE DETECTOR and your mobile phone are being detected by the hub at the exact same moment, it’s likely a coincidence based on some local geography that blocks or strengthens signals. (“Geography” in this case including houses, mail boxes, etc.)
If you set up a similar setup at your grandparents’ house, it’s quite possible the ST device would cover a smaller area than the cellphone detection.
So the ST presence detector is detected when a zigbee signal is successfully completed between your ST hub and the device. Typical range is 50 feet. A zigbee repeater can be used to extend this range another 50 feet or so if needed.
The mobile phone is detected when geolocation services tell your ST hub it’s in range. Typically around 500 feet, but varies, I believe depending on exactly which cell tower pings your phone.