Without ringing them out with an ohmmeter, I'd say that the cheap ones are wired like this=
The Ipod ones SHOULD
be wired like this=
The easiest way to check the wiring on the piece with the ear buds is to take what you believe to be the + and - wires and touch them to a small battery(aa or aaa should work fine). You will hear a small click from the speaker that they correspond to. You can experiment a bit if it doesn't seem right, the battery method won't hurt anything. If by chance the wires(+ and -) get reversed, all it will do is shift the phase 180 degrees out. This shouldn't have much(if any) effect on sound quality though, it matters more when both speakers are sharing the same airspace(as in home stereos and the like).
A final note: make sure you tin the wires on the Ipod ones before you try and solder them to the other wires, they look like they have a lacquer coating on them and they won't want to solder if you don't burn it off first. All you do to tin them is to put the soldering iron on the wire and feed some solder(make sure to use a rosin core solder, not organic or water soluble flux or it'll corrode the wires in no time flat) onto the wires until the coating burns off and that section looks all silvery and shiny.
I hope this helps.