Hi,
Yes they're related, you can read this post it explains it in detail: https://hackernoon.com/what-is-neo-and-what-is-gas-5b9828a1aa65

When you keep NEO in your NEO wallet, it generates some Gas (or you get some gas because you have NEO, which is good for the system- search:"proof of stake") So you earn GAS just by having some NEO. You can check how much you get: https://neotogas.com/

I never bought GAS, but yeah possibly they will grow together.