There are several classes of plants that are regarded to be "pulses," which cover several different genera of plant, originating from different parts of the world; nearly every continent has an indigenous species (although
Australia's is an interesting one.) The terms used to describe them are used differently depending on who uses them. "Pea," and "bean" and "legume" are often used interchangeably, even by botanists. Coloquially, the "pea family" often refers to plants in the genus Pisum, Vigna, and Cicer (English peas, blackeye peas, and chickpeas) Mung and adzuki beans fall into the Vigna genus.
The family Phaseolus, which includes kidney and pinto beans...basically, many beans indigenous to the US - may contain the toxin, which dissipates when cooked. If you plan to eat these beans, you should cook them (or their sprout) thoroughly.
The whole description of a pulse plant is fairly ambiguous: it seems to vary depending on what industry is using it. Agriculturists define pulse plants as any plant that produces an edible seed-bearing pod (which may mean that the seeds are edible, or that both the seeds and pod are edible,) or may expand to include plants which have nitrogen-fixing properties (things like vetch and lupines) however, other sources classify Acacia and Mesquite trees as pulses...and then there's the Australian tree bean. It's a moving target.
http://en.wikipedia.org/wiki/Pulse_(legume)
http://www.encyclopedia.com/topic/pulse_(plant).aspx