difference is a countable noun. Countable nouns in the singular require a determiner.
no is a determiner.
not is not a determiner.
not negates the verb.
So you can have the positive statement
There is with the determiner
no and noun the
difference.
Or you can have the negative statement
There is not with the determiner
any and noun
difference.
But you can't have the negative
There is not and then add
difference without a determiner.
CJ