According to Strategy Wiki:
Developed by Nintendo for the Famicom in 1983 and published for the NES in 1986. It was also made available for the Famicom Disk System as one of the first games purchasable through the Disk Writer system, where players could pay to write games to blank disks. In North America, Donkey Kong was later released on a compilation cart with Donkey Kong Jr., titled Donkey Kong Classics.
None of these original versions contain the Conveyor Belt Stage.
So they look the same game, as it's written.
The only known difference is between the arcade version and NES version, according to Gamespot:
The Famicom (Japan's NES) version of Donkey Kong was actually not a bad game, all things considered. Only one level was missing (in arcades, the third level), but almost everything else was present.
The music was an exact copy of the music from the arcade game. Somewhat strange though were the bizarre sounds Mario made when walking around the levels.
and to Videogameden:
This port of Donkey Kong has a few differences with the original arcade game. First of all, the short introduction sequence was completely removed - in the original game, Donkey Kong climbs the construction site with Pauline under his arm and heavily stromps his feet as he reaches the top, causing the metallic girders to collapse and form the first screen. The 25-meter scale displayed between screens was also omitted - in the arcade game, each screen represents 25m of the construction site, from 25m to 100m.
No, apparently the Japanese Famicom version (ファミコン ドンキーコング) seems to have an English localization: