Since they're both metaphors for a Mystery as cannot be 'explained', and sound as adj. connotes quite a range of nuance.. most of which are a pretty long stretch -
I'd point out one practical difference:

There's some utility to examining the accuracy of personality quirks suggested by 'astrology'. The idea may even be tested in a scientific manner, once one decides what a "competent astrologer" is like, as with a "competent shrink". It ain't all about numbers, you know (as I thought we had been through n times.)

OTOH The only utility I can see of the selling of the ID scheme is - as another soothing wishfulness that, ~ when I Talk to God - SURELY She Will Listen! See? these 'Scientific' Theorists tell me so!

Right: YAN distinctly Chrisian-sect fav ontological proof of god cha cha


(If one is into needing that flimsy a reAssurance re one's chosen God-figure, that is.)