According to Russian Wikipedia
https://ru.wikipedia.org/wiki/%D0%A2-90 :
* T-90AM (obyekt 188AM, program Proryv-2) is a modification of T-90A with new FCS Kalina, improved gun 2A46M-5 with better accuracy, Relikt ERA and remotely controlled 7.62mm AAMG
* T-90MS is an export variant of AM (shown in 2011)
* T-90M (obyekt 188AM, program Proryv-3) is a modification of T-90A. 400 tanks will be "modernized". Gun is 2А82-1М (of T-14 Armata), FCS Kalina.
The same on T-90M is here
https://vpk.name/news/173008_t90_pol...noi_silyi.html ("T90 will get a gun from Armata...")
It is not clear, if T-90AM is used, T-90M is in plans as for now.
Uralvagonzavod received a contract for a batch of T-90M
http://www.vesti.ru/doc.html?id=2926028