A polygraph is not a routine part of the background investigation, but is a requirement for certain agencies/positions.
Originally, no, I didn't need to undergo a polygraph test, but for a specifc job I filled in Iraq I needed to go through (and pass) a counterintel polygraph. Once you have it, though, it's good for a couple years.
And, you're right, S and TS are levels of clearance and the SCI/G/HCS/ are all caveats to it. Add-ons if you will depending on what's necessary for your job.
Awesome, thats what I thought.
Thanks