oudin vs. tesla coils

[CTCDW-at-xxxxxxx (by way of Terry Fritz <twftesla-at-xxxxxxxxxx>)]

Hello folks..

This might be a long winding post, so hang on :)
My question is regarding the difference between oudin coils and "pig" powered 
systems which run with one side grounded. By this I mean that one bushing of 
the tfmr is grounded, as are the bases of BOTH the Primary and secondary, as 
well as one side of the spark gap. I have not done much work with my pole 
trfmr coil, as it became obvious that I should just wait to build a proper 
control cabinet. It seems that there is little difference in these systems, 
since in an oudin coil, as far as I have seen, the primary and secondary are 
attatched together, to ground, and to the other bushing of the transformer, 
which effectively grounds one whole side of the  low voltage end of the 
system... 

Is there an electrical explanation of why these are diferent, if indeed they 
are?

I have heard that an oudin coil uses the primary and secondary as an 
autotransformer, rather than a primary and secondary apart from each other. 
If indeed simply grounding the inner (or bottom) turn of the primary and the 
bottom turn of the secondary together creates an auto transformer, then I 
guess I just learned something :)

Thanks for any insights!!

Chris W