Yeah S05 is Chico yeast - that's pretty well known. It's essentially same yeast as WLP001 or Wyeast 1056.
I've been using that regularly for years. Intimately familiar with it's flavor and behavior.
As for S04 being the same strain as WLP002 - that I do not know and THAT is really my question.
Seems as though it's highly likely. Both ferment quickly, have medium attenuation, and flocculate very well. Both are described as a widely used and/or popular English style Ale yeast. Both are recommended for same English beer styles, ESB, Milds, Bitters, Porters, Stouts etc.
I've brewed a few beers with S04 and WLP002 in the past and I recall being happy with the results but it's been probably 6 years! Guess I've been in a bit if a rut with American ales for awhile.
I'm running to my LHBS today to pickup ingredients for my Obsidian stout clone. Unless somebody can convince me they are the same, I think I'm going to get both yeasts and brew another batch of something else with the S04 another day. I'll make a starter with the WLP002 tonight so it's ready to rock Saturday morning. The Obsidian is pretty healthy clocking in at around 1.070 according to my Beersmith. I followed Jamil's podcast on formulating a clone and had some other information on a recipe from the web too. It was recommended by the brewer at Deschutes to overpitch a bit.