The *distance*, in terms of piece count not meters, to the anchored piece in the ground determines whether you're allowed to add more pieces to something. In other words, 6 pieces sticking out horizontally from a hill is just as weak as 6 pieces sticking straight up off the ground, despite being much closer to the ground. (Keep this in mind when people say the "height" is what matters. The chain distance to the ground, regardless of whether that distance is vertical or horizontal, makes it weak.)

When you attach a thing, the game "walks the graph" of pieces touching other pieces to get a count of the minimum number of pieces it has to traverse before it finds one that touches the ground.

This does get modified by different piece types. Different types of piece (wood, stone, iron-reinforced wood, etc) change the calculation of the "count" in ways that can help. For example, stone parts being stacked on other stone parts still have the same part count limit that wood parts do, BUT, when you chain a wood part off a stone part, the stone part essentially counts as ground for the wood part, resetting its distance count to zero so you can chain wood onto the top of a stone pillar like the stone was the ground.

The reason core-wood poles let you build higher than normal-wood poles comes mostly from the fact that core-wood poles are longer, so it takes fewer parts to chain longer distances.