Tesla have historically provided all cars with premium connectivity without them realising, but from 2019 they have introduced this as a subscription model for some owners. The subscription provides the capability to access some of the car’s features over cellular/mobile networks.
Irrespective of premium connectivity all Teslas come with Standard Connectivity. This allows the cars to receive limited software updates over-the-air (although the general advice is to connect to your home wifi for the fastest updates). Navigation functionality is the same as with premium connectivity except the lack of both satellite imagery and traffic visualisations.
Features such as Bluetooth connectivity to your phone, Radio (not internet radio) and MP3 music are also available as these are not related to connectivity. You also have remote app connectivity to the car. Other than the navigation visualisations, the main functionality that is lost relates to media services such as streaming and Caraoke.
If you opt for premium connectivity you will get Satellite imagery on the map, live traffic visualisation, and media services such as Spotify or Deezer depending on region and streaming radio via services like TuneIn.
For cars that have the necessary hardware (ie M3 and MS and MX with MCU2), services like Caraoke are available.
Essentially, any service that is not mandatory for the core driving features of the car are only accessible over the air if premium connectivity is selected, or if the car is connected to wifi.
Tesla state that all except Live traffic and Satellite-View Maps are available via WiFi including mobile phone hotspots. If you tether your car to your phone wifi you will be available to access these features, however the icons on the map for traffic and satallite view are indeed missing.
One of the issues with Wifi tethering is that as soon as the car was put into drive, the car would disconnect the wifi. This was in part because cars were typically connected to household wifi and when starting in the morning would take time to fail over as you drove away from your house. This was undesireable. Tesla now give the option as to whether you want the car to disconnect automatically from the wifi or not.
Iphones can provide a wifi connection although the car will not automatically conenct. This is a limitation of IoS and the phone must be used to allow the wifi to connect each time.
New cars come with a free trial period, the length of which varies depending ont he model. After that its about $10/£10/10Euro as a guide.