What does it mean to have sacred / ancestral aspects?
This depends on if the aspect was obtained by destroying a sacred or ancestral item.
Does the aspect tier actually matter for anything?
It depends. For some items, as shown, it does not make a difference. However, there are other items where the range does make a difference, and that is in places where applied damage is being used.
For example, with the Sorcerer you can use the Aspect of the Frozen Tundra: "While Deep Freeze is active, exploding Ice Spikes form in the area, dealing [X] Cold damage. Your Ice Spikes have a [30-40%] increased explosion radius.". An aspect from a level 30 item versus an aspect from an ancestral level 80 item will have a significant difference in the [X] Cold damage range (not just the roll in that range, the actual min to max numbers).