Help me understand the difference between ように and ために

Last thread I made was filled with super helpful responses so I am hoping you guys can help me with this question as well.

I have been struggling with the difference here and have been reading a lot of different explanations over the course of the past few days. Feel free to correct anything I write here, or provide your own explanations/examples if you have any.

My current understanding is that ために is used when you want to use a noun, and say you’re doing X for Y’s sake. 息子のために (for my son’s sake)

But with verbs, ために is used for things that are within the persons control (volitional verbs)

However ように should be used when describing things outside of ones control, and is often used with potential form, and ない form? I believe? I understand the potential form, but not really the ない part as I don’t see why you couldn’t NOT do something and still have it be volitional?

I’m still not very advanced obviously so my sentences may be off, but I am going to try to form a few thoughts to see if you guys think they are the correct uses, or if I am off.

**ドアを閉めるために、立てました** (In order to close the door, I stood up) Meaning like I had to get up first in order to be able to go close the door, I did the standing for the sake of closing the door, and I possess the ability to close said door.

**日本語が分かるように辞書を買った** (I bought a dictionary so that I can understand Japanese) or (So that Japanese can be understood, I bought a dictionary)

I have also read that if there is multiple subjects, that it changes which I should be using? As in, I saved up money so X person can travel to Japan, since its me saving money for someone else, it must be ように? but if it was saying I saved up money to go to Japan (myself) I could use ために? I am guessing this is due to the fact that someone else’s actions I lose the volition of the verb, as it’s not me going, its them?

As I said, I am not very confident in all this, and I am more than happy to have any advice, tips or corrections of anything I said here. I appreciate all feedback. Additionally, I am curious if you think https://www.wasabi-jpn.com/japanese-grammar/how-to-express-aims/ this is a good resource for the topic and one I should abide by.