A-yep, those are some tesla coils, Van de graffs are belt-driven static condensors, which still shock you

. Tesla coils on the other hand are
much cooler. In some of those pictures there are two doorknob looking things, I believe those to be spark-gaps, which help control the device. One of those is driven using a neon sign transformer (serious tesla coils use pole pigs

), the other must be using the spark plugs as a charge multiplier

. Basically, they are giant terrifying transformers....so if ya ever get
too scared send them to me

(just kidding, they are great fun).
Just use normal precations and all should be fine. The one on the right (first picture) is certainly the best of the two. I'm not sure how to fix the other, or if its worth it. Plenty of sites out there to building your own (actually quite a bit of math involved).