In an "X is Y" sentence, you can only use the "to" construction, if both X and Y are noun phrases. As here Y is just an adjective, you can only go with "jest".
You may think about "to" as something kinda similar to "=". Let's say that one can imagine "this child = a big child", but not really "this child = big".
As for the first (or rather here: the only one) use of "to", it's a neuter determiner. Better to think about it as a completely different word that just happens to look identical.