I suspect some of those images are different things, but WAGs:
Cassava aka manioc?
Jicama (rather watery)
Or I know nothing about eddoe except that it’s the malanga in the upper right. Doubt that one.
Sorry, all you roots look the same.
What did I eat at a Honduran restaurant that resembled a baked Idaho potato?
carnivorousplant, maybe it was a baked Idaho potato? 
If not, my first guess would be yuca (aka manioc, aka cassava) which is neither a potato nor a true yam.
As for the OP, in Japan potatoes, sweet potatoes, and yams are popular and I can assure you that they are nothing alike.
Potatoes (Solanum tuberosum) and sweet potatoes (Ipomoea batatas) are superficially similar in texture, but quite different in shape. Sweet potatoes being generally longer and quite tapered.
Yams are another thing entirely. The two most popular yams in Japan are the nagaimo (Dioscorea polystachya) and yamaimo (Dioscorea japonica). They may look vaguely like a very long potato, but their texture is completely different, usually described as ‘slimy.’ Nagaimo is often served raw, grated into a goop that is poured on top of rice or noodles. The texture is a bit off-putting at first, but the taste is agreeable.
Yes, yuca.
Thanks!
No problem! I used to have a Peruvian boyfriend who would cook yuca for me all the time. It’s really nice!
Did he bake them? They are available at a grocery store here.
He would serve them to me baked, boiled, or fried. You can pretty much treat them like they were potatoes. His favorite way to serve them was boiled and chilled with Huancaina sauce, like in papa a la Huancaina
Thanks again!
Yup - my gf has cooked yucca as well. Great food!