The Minus K products are based on their patented Negative Stiffness Technology. From a physics point of view, the spring equation is F = k * x, where k is the "spring constant" or "stiffness". Minus K gets their name because they have found a way to implement "negative stiffness" or "minus k" if you will. So, yes, the Minus K system is based on a sophisticated mechanism that includes springs.
I know little about Halcyonics except that it is an active isolator (hence it requires feedback). I just went to the Halcyonics website, and checked their specs, and Minus K still outperforms.
The Minus K set-up is pretty easy, you just dial in the payload (literally, there is a knob and a payload balance indicator), and you're done. It looks like the Halcyonics requires software and other tweaking to make it work.