Normal household general power outlets (GPO) are rated to 10A, so you use the 10A (or the 8A) tail in those. The 15A (or 12A) tail is intended for 15A outlets, which you might have in your garage or shed, but are usually something you specifically request from the electrician. 15A outlets and plugs have a larger earth tang/socket. You can't fit a 15A plug into a 10A socket.
If you aren't already aware, there is also an aftermarket (non-Tesla) 32A tail you can buy for the UMC. If your electrician can install the correct 32A socket, you can then charge at 32 amps, which is four times faster than using an 8A tail in a GPO.