lang.php creates new translatable language strings in your language pack, but what does jslang.php actually do? Does it create a new language strings like lang.php or not? Can these two files have the same strings or not?

jslang.php adds strings on the javascript side and every string you put in there will always be loaded to be available/used in javascript.

@teraßyte will these strings be added into the language pack and become translatable?

If, for example, I need one same string in PHP and JS, should I duplicate it into lang.php and jslang.php?

Yes, the strings get added to the language pack and you can translate them just like usual.