Is there also a version of the venu 3s with mobile radio? Or is there only the one with wifi

If I go running with the watch WITHOUT the smartphone, will everything still be recorded?

For the Garmin Venu 3S with the description "Wi-Fi only", it means that the device does not have an integrated cellular connection (such as LTE or 3G), but only has Wi-Fi and Bluetooth for connecting to other devices and the Internet. This means that the watch must be paired to a Wi-Fi network or Bluetooth device in order to synchronise data or use online functions.