..."What do those abbreviations after the plane type designation actually mean?
Well, abbrevations is so many... For example :

I - Istrebitel' (fighter)
B - Bombardirovschik (bomber)
R - Razvedchik (recon)
IB - Istrebitel'-Bombardirovschik (fighter-bomber)
RB - Razvedchik-Bombardirovschik (recon-bomber)
M - Modifizirovannyi (modernized)
T - Topograf-Radarnyi (old name - radar, seeing the target on background of a ground) or Tanker (tanker)
K - Korabel'nyi (carrier-plane)

And so on. Just ask about concrete modification.

For example, let's take the Su-15TM. What "Su-15" means is pretty obvious, but what does the "TM" mean?
"Su-15TM" was not usual abbreviation.

First of all, this modernization get the new engines (2 x R-13F-300 (+800 kg thrust)) and new radar with new function - seeing low-flying targets (see above).

But second, the name of this radar was "Typhoon-M", so abbreviation of this radar was - "TM".

Of course, second reason is a joke-legend...