Edit: Forgot 6L6 GC STR added it and more material at the end with links to GE publications.
I'm no expert but based on what I've read this is what I think happened. 6L6GC, 7581. 7027, 5881, are all 6L6 family tubes with the following official ratings and similar if not identical transfer characteristics:
6L6 19W I think that these are metal case G is for glass
5881 23 W This is an industrial type power derated 6L6GB
6L6GB 25 W
6L6GC 30 W
6L6GC STR 387 35W By Philips/Sylvania STR is Special Tube Request - See note one below
7581 30 W
7581A 35 W Phillips ECG made a JAN Military version see note 2 below
7027 35 W Pin out is slightly different and may not work in all 6L6 applications
807 is a 6L6 type with a different base and plate cap
There are a few others.
Back in the 60s and 70s production people were learning that common parts reduced production costs. To make a 19W, 25W, 30W, and 35W 6l6 costs more money to set up production for each type. Now, this is my guess, they said why not stuff 6l6 GC, 7581A, with 7027 guts and make them all the same. The lower rated parts will simply have more margin and last longer. Also, companies were pushing the parts right to their limits where they did not last long. Companies that did this would have longer lasting tubes. So, 7027 and 7581A are offically 35 W, some 6L6 GC are 30W and some are truly 35 W with 7027 guts but there is no designation to indicate 35W - you have to look at the guts. Edit, the 6L6 GC STR is a 35W tube so there is an indication. I knew that the STRs by PhilipsECG/Sylvania were 35 W when I wrote this, but not that the STR meant special tube request so the 35W guts were requested by one or more companies, probably Fender. The interesting thing is that Sylvania also did the 35W upgrade to other non STR types so perhaps the efficiency idea hit them at some point. There are modern STRs and I would not count on them being the same.
The reasons are my speculation, but I have read that the guts are positively the same as the 7027 for certain 6L6GC's and those tubes can run all day at 35W on a tester. There is even a tube rated for 19W with 35 W guts.
Also,
5XXX tubes are usually industrial quality tubes
7XXX are optimized for audio use, lower noise and microphonics as I understand it.
The rest are common grade.
KT66 is similar but changes were made that make the transfer characteristics and transconductance different, they require different biasing.
GE publication on the 6L6GC and the 7581, they run them at 80W to show them running red plate:
http://www.triodeel.com/ham1.gif
Continued with a picture of the 5-ply plate material (used in the 6L6 GC not the 6L6GB) that has copper in the core to conduct the heat:
http://www.triodeel.com/ham2.gif
Interesting 1950's paper introducing the 5881 with many features to make it more rugged. It had gold plated grid wire:
http://www.pearl-hifi.com/06_Lit_Archive/07_Misc_Downloads/TungSol_5881_Info.pdf
The Tung-Sol 6L6 GC STR is NOT a 35W tube, at least not rated as one:
http://www.tungsol.com/tungsol/specs/6l6gcstr-tung-sol.pdf
Note 1. - I found this in an ebay add so readers can decide if it is accurate or not:
The STR387 was a "Special Tube Request" by USA amplifier manufacturers seeking a heavy duty 6L6 power tube that would last longer at the higher voltages produced by audio and guitar amplifiers. STR tubes have heavier plates, taller and thicker glass bottles with a higher vacuum so these last up to 4x times longer than imported 6L6 tubes being made today...
Note 2. - There seems to be a military version of the 7581A according to Watford Valves:
https://www.watfordvalves.com/product_detail.asp?id=1317
From that web site, I don't think that all 7581A's are JAN Military:
"Philips ECG JAN / 6L6GC/STR387-7581A-PHILIPS
Philips electronics components group was the name given to the products marketed in America after Philips bought the American valve manufacturer Sylvania in the early 1980’s. Sylvania was a major manufacturer of valves and Philips bought them to get the lucrative American Government and military contracts. These valves are of the highest military grade which offer outstanding performance and were all made in the USA.
The 7581A is the high grade military version of the famous Sylvania 6L6GC STR 387. The 7581A was made to have a higher plate dissipation of 35 watts, where all other 6L6GC types have a 30 watt rating, Philips Sylvania uprated anode plate coating allowing better heat transfer. The valve also uses the highest grade nickel for the anode plate construction so the 7581A gives a long life."
