[2020] Do Passenger Jets land at the International Airport (stock)?

They can land at both. Since they are prefering one over the other, that airport is probably more efficient for them to get to where they're going. The AI tends to pick the fastest route, so using your international airport might just be a slower way to get where they're going.

If you post your city or screenshots from it, you might get some recommendations for what could be done to make your international airport more attractive to use.