No. They are the same. The only difference is that the first one can contain a sequence of three unescaped double quotes, while the second can contain a sequence of three unescaped single quotes. (In other words, because the delimiters are different, there is a slight difference in what characters you can use inside them.)
Docstrings are just regular strings, and in Python there is no difference between the different string delimiters, except that, of course, you can’t use the string delimiter inside the string.