Are all graphics card with the name HD 5770 the same?

Okay there's ATI and Nvidia which creates the boards, and manufactures the boards. Other companies such as XFX, HIS, Sapphire, BFG, etc etc all take the boards and add their own coolers, or custom clocks.. However with new GPU's the cards are all the same, made by ATI (or Nvidia) and resold by those companies with their own packaging etc. The coolers, clocks, and quality are exactly the same the only things that vary with new (release date new) GPU's are the logos, design of the boxes/plastic coverings on the GPU, any extras such as game coupons, as well as the warranty/support of each company.

So to answer your question in simpler terms: For now and maybe a few months they will all be the same until companies begin to mess/make them themselves (adding Fans/heatsinks/aesthetics/clocks/different outputs).