Is the CTFMLA and FMLA two different things?

I called CTPL today, who I'm doing the claim through. They said the same thing HR was saying, that CTPL is only supplementary income and NOT job protection. That even though it is contradictory, my employer has the right to end my employment essentially stopping any sort of supplementary income, at their discretion. I am getting so much conflicting information, I really don't know what to believe.

Thank you, this is what I've been looking for. Does this extend to any state?