The number of turns decides the voltage you get. The size of wire determines the resistance and is one factor in determining the current you get.
Normally you would choose the thickest wire that will go into the space and give the chosen number of turns. Sometimes the ideal wire size is too thick, either to handle physically or with these alternators you run the risk of eddy loss in very thick wires.
In theses cases you can make up the same cross sectional area of copper by using more than one strand of smaller wire and it behaves as if you used the thicker wire but without the problems mentioned. There is no actual gain or advantage except where I have mentioned about the limitations of very thick wire.
Sometimes it is done for other convenience reasons. If you ideally needed #12 but you had a reel of #15 then using 2 in hand #15 would do exactly the same job.
With multiple wires in hand, the turns are decided by the number of times you coil the bunch round the coil. 120 turns of a single wire would not be the same as 60 turns of 2 in hand when connected as you would normally do. It is possible to re connect the 60 turns of 2 in hand to give the same voltage as the 120 turn coil, but it requires you to connect the start of one strand to the finish of the other. It is not normally used this way, but it would be one way of winding for dual voltage ( in low voltage machines only).
Apart from the limitations of thick wire mentioned there is no virtue in using multiple strands in hand. For a given size coil wound for a given voltage you can not get lower resistance by fiddling about with multiple wires. If the size is practical then go for a single wire and have far less ends to bare and connect.
I can't help feeling that to many people this is all a lottery, you will find misleading information if you look hard enough, that is inevitable where hundreds of people post information. The main thing is to get to understand what you are doing so that you can weed out the nonsense. I hope this clarifies the issue for you.
Flux