Or is there something special from the Astral Adventuring Guide that I am missing?
No.
However, the list David42 provided in your linked thread is allegedly the set of attack roll based spells that damage objects, so he left out e.g. Shatter and Disintegrate, both of which will work on ships just fine (remember, the helm is a magic item, but the ship is not). Shatter deals damage, so it will be subject to the ship's Damage Threshold, but Disintegrate will simply automatically succeed at obliterating a 10x10x10 cube in the target ship.
Is the rules for targeting a spelljammer ship with a spell the same as targeting an object with a spell?
https://www.dndbeyond.com/forums/dungeons-dragons-discussion/rules-game-mechanics/75265-what-damaging-spells-can-i-cast-on-objects
Or is there something special from the Astral Adventuring Guide that I am missing?
Yes.
No.
However, the list David42 provided in your linked thread is allegedly the set of attack roll based spells that damage objects, so he left out e.g. Shatter and Disintegrate, both of which will work on ships just fine (remember, the helm is a magic item, but the ship is not). Shatter deals damage, so it will be subject to the ship's Damage Threshold, but Disintegrate will simply automatically succeed at obliterating a 10x10x10 cube in the target ship.