My current take on this:
1) Espressif is a pure-chinese company making the chip (itself based on a "Xtensa LX3 32bit, clocked at 80 MHz" processor design)
Espressif has released some documents labelled 'Confidential', all in Chinese, in the "GongKai" fashion. They communicate a bit in english, their chinese documentation has been roughly translated to english (not sure if that was an individual initiative or under Espressif's direction ?). Espressif seems to be giving attention to the non-chinese channels by running their BBS and posting firmware updates there, and releasing a SDK. All that material and information is pretty rough and bare-bones still.
2) This www.esp8266.com forum is run by a community of afficinados, independent from Espressif, trying to reformat Espressif's rough and tough information in a more accessible-to-the-masses fashion, reverse engineering some of the chip, adapting SW and tools, and building brand new tools and support too (some of those works are truly impressive!). This is done with Espressifs's unspoken blessing and some incidental help (providing SDK, source code, ...)
3) AI-thinkers seems to be a major player for the DIY crowd, they manufacture the ESP-NN family of boards, which integrate a ESP8266 chip and a SRAM, and optionally etched-on or ceramic antenna. Without AI-thinkers, I don't think we could even play with ESP8266 and this whole story would never have taken off as it has.
Apart from that, AI-thinkers is a complete mystery to me, their web site seems to be active but fully in chinese and not at all intended for non-chinese... Are they an offspin of Espressif (probably not because they also have other products), what enticed them to enter (create) that market?
4) node-mcu is yet another mystery, their work on the LUA firmware is awesome, I understand they sell a ESP-8266 board, but I'm not sure of the ties with Espressif. I have difficulty imagining that this kind of work can be done completely independently from the vendor (although maybe it is).
5) there is another crowd of ESP8266-based board makers that is coming of age, with very variable quality, from low-end backplane boards (to adapt 2mm to 1/10" pitch) to renowned board makers such as Olimex, up to awesome boards such as ESPToy (ATMega+ESP-01+CH340+leds and sensors for $25)
Views expressed herein are my own, and I do not claim full accuracy, just best-effort to make sense of all that.
Any precisions or corrections are most than welcome, thanks in advance!
GhW