В чем разница между last и remain ?Пожалуйста, приведите примеры.

They can often be used interchangeably, but in my mind the primary difference is this:

"last" makes me think of position or a step in a sequence.
"remainder" or "remaining" or "what remains" me think about resource consumption.

He is the last person in line. <--- a sequence of people with him in the final position.
He is all that remains of the line. <--- there was a line, but it has been "consumed" and he is what is left

In that example, there is a very different implication. In both cases, the person is the final one, but in one case the line is still there, and in the other, the line is gone.

In this case, the difference is not clear:
This is the last of the soup.
This is what remains of the soup.

In both of these, the soup is almost gone and there is one "serving" left. A native speaker will likely say they mean the same thing, and they probably do. For me, however, the tone is slightly different.

Let's say you are a warehouse worker, and are performing an inventory.
"This is the last of the soup" could mean "This is the last of the soup. I will now count the cans of beans." In other words, with more context, you realize "last" is again being used in a counting sequence.

"This is what remains of the soup. I will now count the cans of beans." sounds strange to me. It's correct, but I would never phrase it this way because for me, "remains" used this way is inconsistent with just counting.

I could say, "I need to count what remains of the soup, and then move on to counting cans of beans." This sounds fine. Count what's left of the consumed soup, and then move on to the beans.

I'm sorry if that isn't very clear. You picked an interesting question. Good luck!