Translation of a field overwrites the original language value
I suggest looking and experimenting with the following settings:

admin/config/regional/language/detection

You can also check if the checkbox "Enable interface translation to English" is checked. That may cause this problem.
admin/config/regional/language/edit/en


Question : One thing didn't become clear for me:
"It is the same as it was before, but on the web page, I have two nodes with different translations." - what is the url of the web page. Is it a page constructed with views, panels, or just node/nid ?
Regards,
Oleg