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".
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".