Ref -- "lamb's quarters" is amaranth, "pig weed" is quinoa. Around here, both are called pigweed, with the quinoa called "red root pigweed", and in other locales, I hear that quinoa is just "red root".
Lamb's quarters is in the genus Chenopodium, and is NOT the same thing as pigweed, which is in the genus Amaranthus. They don't look anything alike.