Jack gave a very good answer.
But I'd like to add that "aid" tends to be a non-human form of assistance.
Like:
Hearing-Aid
or
Financial Aid
Help is a very conversational term that covers most situations.
Both human and non-human.
Such as:
My glasses help me see.
or
Joe helped me open the window.
assist
Help (someone), typically by doing a share of the work.
‘a senior academic would assist him in his work’
help
Make it easier or possible for (someone) to do something by offering them one's services or resources.
‘they helped her with domestic chores’
I often use "assist" in a circumstance when someone need an assistant to help them.
I am not a native Eng. speaker but as far as I know, "aid" is mostly used in a professional tone and not commonly used, but "help" is used in general. "Aid" is used for a specific purpose. For example, The country X is giving millions of dollar in foreign ade to country Y in order to help them fight with their internal disturbances. Mostly, an ade is an economic assistance but in case of help, it may be related to the economy or other kinds of assistance. For example, Are you all right? Do you need any help? Here, if I will use aid instead of help, it sounds weird.
If this is not convincing, then you can wait for some responses from native speakers:)
You can ask questions on the "Answers" forum for quick response.
