> Decomposing organic material in anaerobic conditions — by microbes in the absence of oxygen — releases methane into the atmosphere. Anaerobic fermentation is common in landfill and open stockpiles such as manure piles [azernik: Manure piles are the second big contributor to methane emissions listed in OP.]
The second one just refers to "anaerobic decomposition".
In both cases this is something they mention as the alternative to composting, i.e. they literally define composting by its use of aerobic decomposition methods.
And yes, I agree that this is a complicated biochemical process that should be done by professionals in dedicated facilities (EDIT: which is where most composting happens in California), not in people's backyards. Where did you hear me arguing for amateur backyard piles?