"There is no rule" vs. "there isn't rule"
Solution 1:
The second should be
There isn't a rule.
Rules are countable, so the singular "rule" needs an article or counter of some sort. In the first sentence, "no" counts the number of rules present. In the second "is not" doesn't count, so adding "a" is appropriate.
EDIT: beyond that correction, the two sentences have the same basic meaning. "There is no rule" is more emphatic, but both can be quite strong depending on how they are spoken.
Solution 2:
The second sentence isn't valid. "Isn't" is a contraction of "is not". You could say the following:
There isn't a rule.
Solution 3:
Your question: Are there any differences of the two sentences below:
- There is no rule.
- There isn't rule.
Answer: Indeed, there are.
Sentence 2. uses not in place of the no in sentence 1. More seriously, sentence 1. means there are no rules in place. Here, no is adjective modifying rule. Hence, no rule = absence of rules/a rule. Sentence 2., as it stands, could certainly be made sense of, but it is ungrammatical. Here, not is an adverb that implies the negative and placing a noun such as rule right after it does not work. Others have suggested:
There isn't a rule.
I would also like to add this option:
There isn't any rule.
In my opinion, this is the more commonly used form. Or, even better,
There aren't any rules.
Note that not can also be used in place of an adverbial clause of negation:
- Is there any rule against this?
- There is no rule/There isn't/No, there isn't/There isn't any [rule]
Solution 4:
As Jimi says, the second can be made sense of, and it's even (IMPSO) grammatical. To wit:
There's isn't rule [of law].
Not something I'd say, but I think it's correct.