is a yam a potato or a grain?
A yam is a root, so it’s clearly not a grain.
Like a potato, a yam is a tuber. At least it was when I was in grade school…
A tuber? I thought it was more like an ocarina. 
What is generally called a yam in US supermarkets isn’t actually a yam. It’s a variety of sweet potato (Ipomoea batatas). It’s not very closely related to the potato.
The true yam isn’t very closely related to the potato either.
All of the above are tubers.
OK, trying to answer the OP:
True yams in my neck of the woods are sold under the name ñame. They’re a member of the lily family.
Sweet potatoes are sometimes referred to as “yams,” but mostly in the context of “candied yams.” They’re a member of the morning glory family.
And neither are grains.
But, if you’re asking where a yam would fit under the classic “four food groups” model, it’s not meat and it’s not dairy. So is it a fruit/vegetable, or a “bread and grains”? It could be either, but since it’s mostly starch and sugar, it would fit into the “cereals” category. But so would all sorts of other vegetables that are mostly starch, like potatoes.
Moved to Cafe Society.
Call it bread or starch rather than grain.
And sweet potato/yam is better for you than white potato. It has a much lower glycemic index, and doesn’t jack your blood sugar up as high or as fast.
~VOW
[Popeye]I yam what I yam.[/Popeye]
[ahnold] It’s not a tubah![/ahnold]
The subject line doesn’t look right without a couple of exclamation points after it.
I’ve been here for four years, lurked a bit before that, and I still think yams!! is my favorite username on here, and I even love the sig of “love, yams!!”