We don't say "There is not". We say: "There isn't any...." or "There isn't a ......." You need to pay far more attention to what you read! There isn't any water. There's no water. There aren't any people. There are no people. They mean 98% the same. The difference is minor.

Actually in colloquial English, especially where I'm from, "there's not" is a common usage, but only as a repeated interjection; "There's a spider on your neck!" "There is not!"

Let me just give an alternative point of view to the previous answers. "There's not" = "There isn't" So you can say things like, "There's not any difference..." or "There's not any change in meaning ... " It means the same as "There isn't any difference..." or "There isn't any change in meaning." Using "there's not" like this is probably more common in conversation than in writing, but that doesn't make it wrong. If you google the term "there's not any *" millions of results come up. However, you cannot say "There's no any..." Just say "there's no" + singular noun. There's no milk. There isn't any milk. There's not any milk. Hope this helps!