Assuming you are talking of a 32A blue socket, for practical purposes the same (about 22mph). The wall connector can go faster if you have a three-phase supply to connect it to, but that’s unlikely.
If you were talking of the smaller 16A blue socket (as used with caravans), then that’s not directly supported by the Tesla UMC but if you made up an adapter it would charge at half the speed.
Electrically, the Mobile connector UMC and the Wall Connector are the same thing: the WC is in a more robust and weatherproof housing, but you could in principle install a blue socket and fix your UMC to the wall and have the same thing as a WC. However, you’d then have no UMC to take with you for charging away from home. Alternatively, you unplug it each morning, roll up the dirty cable and take it with you (tiresome); or you only do that when going on a trip, and end up forgetting it the one time you critically need it.
It’s also better if your UMC isn’t your daily use charging solution, as if it ever got damaged or faulty you would up in big trouble.
BTW, if installing that blue socket, it neds exactly the same wiring and to follow the same regulations (Type A RCD, earthing) as if you were installing a WC. It does of course save the cost of the WC itself.
