North and south magnetic poles are named after the north and south celestial poles because they seem to coincide. That doesn't apply to the solar poles.

People always make use of local geographic features when describing directions; river communities use "upstream" and "downstream" and island communities use "inland" (away from the sea). Those aren't termed poles (even though "inland" is defined by reference to a line perpendicular to the ground!), and while I agree that the axis of orientation to the sun is more pole-like than they are, it's still different enough that I don't see that it would necessarily be referred to in the same terms.

You don't have to look to rural tribes to find this behavior. In Manhattan, "North" and "South" usually are colloquially defined with respect to the orientation of the island, not the actual compass directions.

And here in the vicinity of Santa Cruz, and going up towards San Francisco, "north" and "south" are often defined by reference to the labels on a freeway, even when that freeway in fact runs east-west.

Doing that in the Bay Area can have some odd results, as (for example) there is a stretch of freeway that is simultaneously I-580W and I-80E (and vice versa). Naturally, it runs almost due North and South.

> North and south magnetic poles are named after the north and south celestial poles because they seem to coincide.

Sure, and that's why the axis-to-the-star probably wouldn't define "north" and "south" poles, but not a reason it doesn't make sense to call that the points where the surface intersects that axis through the planet "poles".

That all depends on how some not-particularly-advanced people feel about it when the terms are determined.

Having thought a bit more, I tend to think it's unlikely that both axes would be significant to the same people (and therefore that they are particularly unlikely to share terminology):

- One important aspect of east-west historically is that east is sunrise and west is sunset. This wouldn't matter to anyone on Tidelocked World, but it corresponds pretty well to the idea of having a Day Pole and a Night Pole. The Day Pole would be apparent to anyone who lived in an area where the sun was visible, and the Night Pole would be totally unapparent to everyone else; it is significant only in that the Day Pole is on the opposite side of the world.

- Historically, north is cold and south is hot. This would apply, I believe, only to the day side of Tidelocked World. It reinforces the idea of a Day Pole while doing nothing for the Night Pole (everything beyond the terminator should (?) be equally cold).

- North and south are also defined by reference to the stars, which rotate around the polar axis (this is the origin of the word "pole", and would definitively rule out a Sun Pole if "poles" had to be defined that way, which they don't). This would be apparent to everyone living in the night, but probably not to anyone in the day.

If you believe all that, then we have the sun as a navigational aid that guides us toward the hottest part of the world, and the stars as a navigational aid to indicate the North and South Poles, but no concept of a Night Pole, because that concept is useless on the night side and there are no local indicators for where it is. Day people would be likely to refer to "sunward" and "darkward" in the manner of islanders, and night people would likely refer to "north" and "south", but day people would be unlikely to recognize "north" and "south", and night people would be unlikely to recognize "lightward".

>everything beyond the terminator should (?) be equally cold

I don't think so. Winds, diffusion, conduction, refraction probably come into play.

Sure. How much variation do you expect as a function of distance from the terminator? Other sources of variation aren't really relevant.

It does occur to me that the Night Pole might be revealed by the shadow of the planet, if it has a moon.