Why do primary coils differ in shape and location between different Tesla Coils?
I've seen reverse cone, cylinder, perpendicular spiral, and just wrapped haphazard. You can see which coil is primary in the following images, as well as examples of different styles of wrapping for the coils. I've also seen the primary coil placed at the base of the secondary, as well as in the center of the secondary.
I've gathered the following information in my research (I'm pretty sure everything is correct):
The primary coils, through induction, transfers the charge to the secondary coils.
The primary coils are much thicker to allow for the large amounts of current running through them.
For maximum induction, you want the same amount of surface area for primary and secondary coils (I've seen this written in different ways at different places). (You don't not want Maximum Induction see: steveastrouk's comment below)
Primary coils are placed in a way to allow for....... (this is where things start to fall off and the reason for my question).
So, if your goal is to have the most charge transfered from one coil to another, why are there so many different styles? Does one style benefit over another? Is there a logical reason one would opt for one one style rather then another?
Image 1: parts information
Image 2 & 3: cylinder and cylinder centered
Image 4: wrapped haphazard
Image 5: reverse cone
Image 6: not sure
Image 7: perpendicular spiral