You have a little catching up to do! Here's the summary.
The mobile charger is a Level 1 charger and is for charging from AC power points like the typical 10A (10 amp) general power outlets in your house, or 15A power points like might be in your shed or a caravan park. Your kit will have two swappable tails so that you can plug into 10A and 15A power points. You can also buy a third-party tail that can charge at up to 32A. To work out how many kW you are receiving, multiply the voltage (usually 230V) by the amps. If you charge at 230V and 10A for one hour, you will add 2.3kWh to you car (although it is actually a bit less due to inefficiencies).
A Level 2 charger (like the Tesla High Power Wall Connector, or a destination charger at a hotel or shopping centre) also charges in ACz but at a higher rate. The Model Y can "only" receive 11kW of AC. Those chargers provide their own cables in most circumstances. There are some that don't, like the AC units that act as backups on the Qld Electric Superhighway chargers. For them, you need to BYO a "type 2 to type 2" cable, which can also be called "Mennekes". You never use your mobile charger at a public charging station, but you might use it at a caravan park or cabin, friend's house, etc.
Level 3 charging is DC charging at higher speeds, and the cable is permanently attached to the charger. This includes Tesla Superchargers, Evie, Chargefox and other providers. You don't need to provide your own.
If you haven't already, it is a good idea to familiarise yourself with the apps "A Better Route Planner" and "Plugshare". Plugshare is excellent for learning the state of non-Tesla chargers, and communicating with other EV drivers using the chargers. You should probably did which charging networks are in your area and setup their apps. Even if you plan to use superchargers, it is worth being familiar with the other networks so you have more options.