For Recover, which is primarily an online resource for health care and public health professionals, the smoke was created with binary code, a series of ones and zeros laid over each other until nearly black at the bottom and light and ethereal at the top. Here the Arial type is filled in with blue sky and clouds, symbolizing the clean breathing that will be the result of physical recovery from exposure. The URL is part of the logo, adding more context to the binary code background.
For the LMPHC, the 'rising from the smoke' concept was paid off with the literal smoke of ground zero in a moving photo taken by Photographer's Mate 2nd Class Jim Watson of the U.S. Navy. (which means it's in the public domain)