Two systems of counting stars. Which ones are the same in both?

[remotemass]

Consider two systems of counting/naming the observable stars, A and B.
In A we start with the Sun which will be "Star 1", then we have "Star 2" that will be the closest to the Sun, then "Star 3" that is the second closer to the Sun, and so on and so forth.
In B, we also start by calling the Sun "Star 1" and "Star 2" will also be the closest to the Sun, but then "Star 3" will be the closest to "Star 2", "Star 4" the closest to "Star 3", and so on and so forth.
Which starts, apart from "Star 1" and "Star 2", will be the same stars in A and in B?

p.s. I got inspired by the beautiful image of connected stars at: http://ethereum.org/

[Phinnaeus Gage]

Consider two systems of counting/naming the observable stars, A and B.
In A we start with the Sun which will be "Star 1", then we have "Star 2" that will be the closest to the Sun, then "Star 3" that is the second closer to the Sun, and so on and so forth.
In B, we also start by calling the Sun "Star 1" and "Star 2" will also be the closest to the Sun, but then "Star 3" will be the closest to "Star 2", "Star 4" the closest to "Star 3", and so on and so forth.
Which starts, apart from "Star 1" and "Star 2", will be the same stars in A and in B?

p.s. I got inspired by the beautiful image of connected stars at: http://ethereum.org/

Holy shit! I can incorporate what I envisioned earlier today with this damn thing: https://bitcointalk.org/index.php?topic=431248.0