pretty sure the in canon explanation is that the seeds are supposed to be like acorns and just kinda sit around untill something gets it into the ground

Wheat and similar grains are all the consequence of human intervention. Wild wheat was originally indistinguishable from common grasses. Through thousands of years of our ancestors growing these plants for food, and then selecting and replanting the ones with the biggest seed heads, or the most disease resistance, we arrived at the modern wheat that we all think of.

Wait that means zombies are also made of iron and carrots what

This also means that zombies are atleast partially made of potatoes

Wheat would definitely have to be a type of grass but not all grass would be wheat :).

wheat is fancy grass, and grass is un-fancyfied wheat

Wheat is indeed a grass, as are barley and rice.