What PCB wire termination should I use for high-vibration environments?
Not having heard of either of these devices before, I did a bit of research into these parts. 

To answer your first question, no, they are not the same part. A "spring cage, tension clamp" connector seems to be just an ordinary terminal block, which is not what you want.

As far as being the "correct" part, there seems to be no one solution to this problem. I am sure that there would be lots of ways of connecting a wire to a bord in a high vibration environment. The Wago cage clamp seems as good a solution as any, and looks pretty robust and well-made. I don't know how much they cost though, and it us probably worth looking around in case another manufacturer has a similar part cheaper and/or better suited to your individual project.