Korobeyniki is not a folk song; it is a late 19th century poem by Nekrassov about a peddler haggling with a girl and in the end he does imply that they had sex. That became a street song I do not know when but in the West it likely gained notoriety in the 1980s as Tetris music and to the programmist of Tetris, Alexey Pajitnov, it was likely known through such performers of street music as Arkadiy Severnyy.

Kalinka in Russia is associated with "Klyukva", or the à la russe kitsch that is sold to tourists and is performed in Russian restaurants abroad as Russian folk culture. I presume it has it's roots in holywood or earlier even in Jules Verne and the likes. By the way, I notice certain bits of foreign culture are also known more widely in Russia than in the respective country. For England it's Child ballads about Robin Hood and "we’ll tak' a cup o’ kindness yet". For Germany it's "Augustin". For France it is the songs by Béranger.