There's no difference between the two. You can use either I don't have or I have no when constructing a negative sentence or negative sentences. 

Example:

1. I have no idea

2. I don't have an idea. (on this sentence, always remember to use AN/A before object of the sentence) .

** AN (vowels) - any words that start with letter A, E, I, O, U 

** A (consonant) - any words that start with letter B, C, D, F, G, H, J, K, L, M, N, P, Q, R, S, T, V, W, X, Y, Z. 

It's important to remember that ‘have’ can be a main verb or an auxiliary verb. If it's a main verb you need another auxiliary to support it, such as ‘do’. ‘Do you have a new car?’

When it's an auxiliary verb it's helping another verb – ‘Have you got a new car?’ But please try to avoid – ‘I haven't a new car.’ 

There is no different meaning. But if you want to impress the negative sentence, you should use "I have no somthing".

on my opinion,the former means I have never do something,and the rest means I don't own anything.it's the differences between  behavior and materials.