What’s the difference between modals and the English subjunctive?

1. “He should go”. = “It is necessary that he go”.

Is the sentence with the modal a subjunctive? If not, what is it?

And what about the other modals, “can, would, could, will”.

Also, in the imperative mood:

1. “Do your homework!”

2. “You must do your homework!”

3. “It is required that you do your homework!”

What are the sentence moods of the above sentences?

Basically, I need to know the difference between modals and the subjunctive/imperative mood. Thanks.

There is a consistent relationship with the subjunctive and the modal "would" (the verbs in the subjunctive mood are in yellow)

If I were you, I would read the referenced link.  >> Past subjunctive in the if-clause, modal "would" + present in the main clause.

If I had known the link location, I would have posted it.  >> Past perfect subjunctive in the if-clause,  would + present perfect in the main clause.

In expressing wishes, the modal would + subjunctive can be used:

I wish you would stop talking so loud. >> (a wish for the future; modal "would")

She wished that he had asked her to marry him. >>(a wish for the past)

I wish you were here with me.  >> (a wish for the present)