1/ The engines are called AL (Архип Михайлович Люлька) because they ALL start from a common base and design office (Lyulka). The Salyut/Saturn distinction is irrelevant as they both work within the
ODK holding company.
2/ The Su-27's AL-31F will give rise to the AL-31FP, which is distinguished by the presence of vectored thrust nozzles: the power between the two models is identical... while the Su-34 is equipped with the AL-31F (Izd.99V) identical to that of the Su-27. As a result, the three engines develop the same thrust: 75.2 kN dry and 122.6 kN in PC mode. The difference lies in the presence or absence of vectored thrust (AL-31FP: with / AL-31F: without). The ‘132 kN on the Su-34’ story is the result of an (old AND unrealized) project to re-equip the Su-34 with the AL-31FM-1.
=> What's more, the Russians are transparent: Rosoboronexport even indicates on
its website which engines power which aircraft.
3/ The J-10B is equipped (at least initially) with an AL-31FN, the main modification of which is that the reduction gearbox is located in a lower position (unlike the ‘Russian’ variants). This would make the aircraft slightly more powerful, although this has never been officially confirmed. There have been ‘discussions’ about AL-31FN ‘series 2’ and ‘series 3’, but to be honest it smacks more of Sino-Russian forum jibber-jabber than factual information. The J-20? No idea.
4/ The AL-41F1S (Izd.117S) is designed above all for the Su-35S. It is above all an in-depth work on the AL-31F with a new hot section in the engine. It develops 86.3 kN of dry thrust (compared with 75.2 kN on the AL-31F/-FP), 137.3 kN of PC thrust (compared with 122.6 kN on the AL-31F/-FP) and 142.2 kN of emergency thrust. Eventually, the Russians plan to standardise the Su-30SMs brought up to the Su-30SM2 standard with the Su-35S's Izd.117S, but the Su-34 should in theory switch to a dedicated variant of the AL-51F-1 (Izd.30), i.e. the second-stage (and therefore definitive) engine for the Su-57. It should be noted that the ‘definitive’ version of the Su-30SM2 with new engines is still awaited...
5/ The Su-57 in its current state has AL-41F1 (Izd.117) engines, the main difference between which and the Su-35S lies in the latter's control mode (integrated or not into the flight control system). Eventually, the Su-57M (unofficial designation) will be fitted with the AL-51F-1 (Izd.30).
In short, didn't you get anything? No problem!
Let me summarise.
Su-27/Su-34: AL-31F.
Su-30SM: AL-31FP.
Su-30SM2: AL-41F1S.
Su-35S: AL-41F1S.
Su-34M: variant AL-51F-1 (+/- long term).
Su-57: AL-41F1.
Su-57M: AL-51F-1.
In short, it starts with ‘AL’, it has a ‘1’ and an ‘F’ in the designation, but basically, it has nothing to do with anything.
As far as India is concerned, apart from a rehash of the AL-31FM-1 project (which is unlikely, and what's the point, given that it was never completed), I can't see what the Russians are going to come up with: either it'll be an AL-41F1S, but that will require a lot of work because the points at which the engines are attached to the airframe differ between the Su-30MKI (which gave rise to the Su-30SM/-SM2) and the Su-35S, or it'll be an AL-31FP on steroids but without any major changes.
Sorry to say but most of this is wrong. Lulkya is Saturn, NPO Saturn is a merger of Lulkya-Saturn and Rybinsk Motors. Now it's called UEC NPO Saturn or just UEC Saturn. It's only a designer, not a producer.
Salyut is a producer, but also designs stuff on their own.
For example, ADA designed LCA, similar to how Saturn designed AL-31F. And Salyut and UMPO are the producers. While UMPO produces engines designed by today's UEC Saturn, Salyut went a step further and have also made their own modernizations. So Salyut's similar to HAL, in terms of how ADA developed LCA Mk1, but HAL went a step further with Mk1A on their own.
Similarly Sukhoi designs jets, but the producers are Irkut, NAPO and KnAAPO. Irkut produces Su-27UB, Su-30K, Su-30MKI, MKA, MKM, SM and SM2 while KnAAPO produces Su-27, Su-30M/M2/MKK/MK2, Su-35S and Su-57. Su-34 is produced by NAPO. So there are three of these Flanker derivative manufacturers, which explains their high rate of production. At more or less 1 regiment each, they have production capacity for 60-75 jets, which they are expanding to 100 per year. I guess it's 'cause they added the Su-57 line as well.
India works with Saturn+UMPO/Irkut while the Chinese work with Salyut/KnAAPO.
So AL-31F has two branches. One directly by Saturn with AL-31F, FP, AL-41F1 and AL-41F1S whereas Salyut designed the AL-31FM and AL-31FN families.
While the FN is used by J-10, the FM series was developed for Su-34, S-27M and Su-30M2 for the Russian air force. AL-31FM1 has a slightly increased inlet diameter of 924mm vs AL-31F's baseline 905mm, it increased thrust to 132 kN. They used a new core similar to the AL-31FP's generation which increased TTSL to 2000 hours. Then an AL-31FM2 was made for the J-20. Prototypes and early LRIP models used it. Its thrust was increased to 142 kN and TTSL was 3000 hours.
FM3 was special. It went through a long development process as Saturn's AL-41F1 did, with new cold and hot parts. It was designed to generate a thrust of 147 kN and competed with AL-41F1 for Su-57 and lost.
Salyut's derivatives are a cause of friction with Saturn who have accused Salyut of IPR theft. When it comes to India, we will obviously not use Salyut's tech designed for the FM family. Saturn's pushing for AL-41F1S for the IAF's MKI MLU, but it's obvious they will have a simpler modernization for the AL-31FP instead.
Similarly, Irkut and KnAAPO competed for the IAF MKI contract too. While Sukhoi and Irkut modernized the Su-30M with Su-37 tech, KnAAPO took their older Su-30MKK and modernised it to the same standards as MKI on their own, with pretty much the same avionics, like the Bars radar. It was called Su-35UB. After the IAF failed to show interest, they offered it to the Chinese when they were whining about J-11A being inadequate, who rejected it citing the use of experimental tech, but had different plans via J-11B.
While I never brought it up before, I'm sure internal rivalries between Irkut and KnAAPO played a significant part in scuttling IAF's FGFA, 'cause HAL had to partner with KnAAPO this time, using MKI production tech supplied by Irkut while Irkut was pressuring HAL to keep the MKI production going. And now, Irkut seems to be keen on using HAL to circumvent CAATSA for Su-30SM/SM2 while eventually placing themselves as the future partner for any new Su-57 program with the IAF. So if the IAF buys 40-60 jets, they can then circumvent CAATSA for the Su-57 as well.
When you look deeper, there's a lot of dirt under their aerospace industry. UAC and UEC were created to end such ridiculous rivalries so things are a lot cleaner now. Irkut is now called Yakovlev as of last year and has their own design bureau similar to Sukhoi. So now that there's Yakovlev and Sukhoi, Mikoyan is being subsumed into Sukhoi.