I believe houses are fed 3 phase supply in the street and adjacent houses get the 3 phases to balance load.
In a commercial unit, if taking single phases from the Distribution unit I believe precaution is needed where there it’s possible different single phases are run around a factory - not sure why.
Correct! As it progresses along the street it, to each house in sequence, it would be Ph1; Ph2; Ph3; Ph1; Ph2;Ph3 and so on all the way along. It could even be two adjacent houses on each phase, the idea overall - is that there should be a near equal load placed upon each of the three phases. A perfectly balanced load means there would be a minimum of current flowing in the neutral. Often the neutral will be smaller than the phase conductors, because due to the load balancing - it isn't needed to carry that much current. Should that neutral fail (and it has been known), it then becomes possible for a lightly loaded house compared to others, to find its supply rising to near 415v.The neutral is the common conductor which will go to every house in the street.
Phase to neutral the voltage is 240v (yes I know230v, but this is the UK), phase to either of the other two phases it is 415v. In factories, offices and similar where 3ph is often available, care needs to be taken to ensure areas which have a 240v on one phase, are reasonably segregated from areas in which another phase is in use. What you don't want is a cleaner pushing one faulty vac around on Ph1, also grabbing a second faulty vac which is plugged into another phase - otherwise, they get 415v across them.
Ph1 in one factory, might not even be the same ph1 conductor in the adjacent factory. All that really matters is the 'phase rotation' to the factory owners, or the 'firing order' of the phases in relation to each other, for 3ph motors. Get a wrong combination and the motor goes backwards, with a 50/50 chance of getting it right or wrong.
Easy to correct on a small motor by simply swapping two of the phase wires over, but on some of the big stuff I regularly worked upon - you checked the phase rotation and made sure the motor went the right way first off, because they were so difficult to change heavy cables over. Even then, some machines mechanically should not be rotated the wrong way, so if in doubt - you disconnect the coupling.