There is a little water in the pot.
There is some water in the pot.
What is the difference between them? How can I distinguish these sentences? I am a bit confused.
"A little" has greater emphasis on there being a small amount than "some." In that sense, "a little" is less than "some."
For example, someone who leaves a pot on the stove for far too long and comes back might say "there is a little water in the pot" to express greater relief at a near miss of a much more dangerous situation, than "there is some water in the pot" which someone might say when there's still plenty left - not too much that it's in danger of boiling over, and not so little that it's in danger of burning.
There really isn't much of a difference. Saying there is a little water is like saying "there is a small amount of water," while saying there is some water is just saying there is an arbitrary (unknown or unspecified) amount of water.
"A little" can be confusing, since people who don't speak English primarily might confuse it with the word "small". While "little" means "small", "a little" usually refers to "a small amount". Saying "There is a small water in the pot" doesn't make sense.
If this doesn't answer your question, or you need more clarification, just let me know.