Type 3 charging point? Do you mean Mode 3, ie an AC home wall connector/charge point? Nobody bothers with different Mode terminology, its not important to know that a UMC is Mode 2 and a Wall connector/charge point is Mode 3 (DC is Mode 4 for completeness) . What is important is that your car comes with a couple of Type 2 solutions for AC charging. For DC, its all attached to the charger.
Its pretty simple. Type 2 for AC, CCS for DC.
For AC (up to 11kW on Model 3) its Type 2, either your own cable, or tethered to the charge point. The Type 2 is European standard since around 2013 for public charge points so you probably will not encounter the other AC cable, a Type 1, except on non public charge points owned by people with typically a Japanese EV.
For DC (typically > ~50kW) it is CCS which is always connected to the charger. You sometimes have to choose between the CCS cable and another, but CCS is easily recognisable.