Nisaba makes an excellent point. Both cards can relate to healing from an illness or injury, as well as anything else, but the Star is "There's your goal in the distance; it'll take work, but we can reach it." It comes at the beginning, and it's focus is to show you that there is a hopeful future in the distance; it's not guaranteed, but its possible if you're willing to go that way. So you've been given your first dose of medicine, a glimpse of what you might have, and assurances that you can reach this hopeful conclusion if you want to.
Judgement is "We can get you out of this hospital, but only if you're willing to face this one thing that you haven't been able to face." Judgement comes up not at the beginning of something, but at a point near the very end. The name and image on the card is, after all, that moment just before accession to heaven, the *last* judgement.
In Judgement, you're gone every step of the journey, done all the work to get yourself to this point. You're one step away from the end, but you've hit a major roadblock. One that requires you to face something or admit something or let go of something you've been holding onto this whole time. It's the hardest thing of all to let it go, but now you have to decide, let it go and get to your goal, or hold on and stay where you are. Judgement is that moment of decision with the promise of complete healing if you do let go.
Judgement present that qualification. If you don't do this, you don't ascend.
The Star's only qualification for healing is that you accept a drink of the waters it freely offers and be willing to head toward that distant future.
