Your second and third show the two ways to connect a single phase, but you show it with different scales. The issue is also confused somewhat by having round magnets and coils which implies an axial design and it is a bit remote from the normal single phase discussion to machines in general.

I showed the same thing as it would be done with a radial machine and with the same size magnets.

For a motor or a conventional iron cored alternator where resistance is no big factor the windings would be equivalent and interchangeable . The first has half the coils but each coil contains twice as many turns. The second twice as many coils each with half the turns. The turns/phase is the same in each case and the winding area is the same and the total wire csa is the same.

The only difference is that the first version will end up with a longer length of wire and will have a slightly higher resistance and for axial air gap things with no reacance the lower resistance winding will perform a little better. As Ed said the version with the same number of coils as magnets will do a bit better.

Sorry if I think in terms of normal machines, the rest of the world does as well. If you learn all your machine theory from what is done here then you will meet with strange reactions from engineers brought up on conventional machines. These ironless axial machines are odd by any normal standard and sometimes you have to think about the implications of the changes. The addition of rectifiers to any alternator puts it into the realms of special and again the implications are difficult to deduce from conventional experience.