What is the difference between "intertwine" and "interweave"?

After looking up the words, I'm unable to come up with an objective difference, other than what has already been described as the difference between the verbs twining and weaving. So this answer is admittedly very subjective.

1. Intertwine implies a circular, twisting, or rotary motion. Interweave implies a flatter, back-and-forth or up-and-down motion.
2. Both words tend to be used metaphorically...
3. Metaphorically, intertwine tends to be used when describing just two things. And it carries a little bit of a negative or difficult to separate connotation. "The man and his wife were intertwined in a pattern of co-dependency."
4. Metaphorically, interweave tends to be used when describing two or more things. It carries a less negative connotation, and the implication is that the interactions are more complicated and intricate, but not necessarily difficult to separate. "The board members interweaved a complex dance of negotiations."
5. As far as I can tell, "entwine" has the same denotation as "intertwine," but entwine tends to be used in more positive situations: "The man and his wife were entwined in an embrace."

A "weave" is an X-Y grid of threads, half running vertically, half running horizontally (in the simplest case), with the vertical thread running under one horizontal thread then over the next, such that a "fabric" is produced. The threads are interwoven.

Intertwined simply means "tangled", such as vines might become when several vines are growing near each other.

Twine is braided; weaves are woven.

A braid (also referred to as a plait) is a complex structure or pattern formed by interlacing three or more strands of flexible material such as textile yarns, wire, or hair. Compared with the process of weaving, which usually involves two separate, perpendicular groups of strands (warp and weft), a braid is usually long and narrow, with each component strand functionally equivalent in zigzagging forward through the overlapping mass of the others. –Wiki.

Colloquially there's little difference but in terms of material science, it's one or the other.