Asian Amaranth is the vegetable type that is grown as a leafy vegetable (Amaranthus tricolor) It does of course grow a seed head but the heads and seeds are small. several varieties are available form vendors of Asian seed. http://www.evergreenseeds.com/edamyintsach.html
Grain Amaranth is of American origen and refered to as Mexican grain amaranth. http://www.uky.edu/Ag/CCD/introsheets/amaranth.pdf These will be be the species cruentus or hypochondiacus. While grown mostly for the seed heads, I understand the leaves are also edible. A liitle more difficult to find a seed source, but there are a few vendors.http://sustainableseedco.com/amaranth/ I would suspect that these may be more suitable for double duty.

Okay, I'm going to go out on a limb here and ask that stupid question: What about the weed-amaranth? Can't you eat the leaves and seeds of those? How do they compare to the "bred" amaranth? I've seen asian folks picking these at parks, etc.

yes. actually most weeds are edible if you are hungry enough. the most common wild version of amaranth is pigweed. http://www.foragingtexas.com/2008/08/amarath_20.html

Here is a link that might be useful: amaranth

Amaranth seed is also available from Botanical Interests. I picked up a packet of Amaranth Burgundy last year at their booth at a fair and hopefully will find a space to plant it.

Here is a link that might be useful: Botanical Interests, Amaranth

Try buying a sack of amaranth seed from the health food store and planting those. You get a lot more seeds that way and still have plenty leftover to eat after planting unless you plan to plant acres of it. I've heard that the blond colored seeds are better eating than the black colored seeds. Its my understanding that the yellow headed varieties produce the blonde colored seeds. I grew amaranth for the first time this year and it was a red headed variety with black seeds. I didn't get enough seeds to eat but got more than enough to plant a huge patch next year. The leaves were good after steaming, very similar in texture to spinach. Very few bugs bothered my plants but mice did start to dig into the seed heads after the bulk of the seeds matured. Don't wait to harvest! Spiders liked hanging out in the protection of the seed heads. They will grow in poor soil and may get 3 foot tall - like mine did. But you can get monster sized plants with huge seed heads in good soil with plenty of water. I found they companion plant with beans well whether viney or bush type but the beans do attract pests. Threshing the seed heads is a lot of work but winnowing is dead easy. You'd think that with the seeds so small they'd blow with the chaff but the chaff is so light that just a puff of air from you is enough to blow it off. I winnow using a plastic gold panning pan.