Yes, all 3 phones have different LTE frequency band coverage according to GSM Arena:
http://www.gsmarena.com/compare.php3?idPhone1=8580&idPhone2=8531&idPhone3=8291
Now I got the entire sequence of events.
1) In Aug 2016, Xiaomi launched RN4 MTK X20 in China, they called it Redmi Note 4
2) In Jan 2017, Xiaomi launched RN4 SD625 in India, with 3 LTE bands, they also called it Redmi Note 4
3) In Feb 2017, Xiaomi launched RN4 SD625 in China, with more LTE bands compared to India launch, this time to avoid confusion with the existing MTK version in China, they called this Redmi Note 4X.
4) In Mar 2017, this RN4X is the international version which was also launched in Singapore and called as Redmi Note 4.
So basically the local set that we get in Singapore is really RN4X. So on a broad level there are only 2 versions, the original MTK version and the SD625 version. For the SD625, 4 or 4X can be used interchangeably depending on whether you are in China or not in China

Also the LTE bands on the SD625 can vary depending on whether it is India set or international set. The Russia version also supports same bands as the Singapore version.
https://translate.google.com.sg/translate?hl=en&sl=ru&u=http://www.mi.com/ru/note4/&prev=search