Which two? I'm near-fluent in Korean and I definitely think differently when in "Korean mode" than when I'm speaking English. But when I've studied e.g. Norwegian, it's so similar to English that there's not much of a change.
It's worth noting that they are from the same linguistic family. Having studied Latin, to me Russian seemed pretty familiar conceptually once I got past the whole cyrillic thing. I am admittedly nowhere near fluent, and I realize the experience would be different for someone without previous 2nd-language exposure.
About the modes, did you by chance have Russian exposure during childhood (guessing based on your id)... that might account for some degree of integration even if you only became fluent later.
what were the languages? they may be very similar.