str.count() counts non-overlapping occurrences of the substring:
Return the number of non-overlapping occurrences of substring sub.
There is exactly one such place where the substring '' occurs in the string '': right at the start. So the count should return 1.
Generally speaking, the empty string will match at all positions in a given string, including right at the start and end, so the count should always be the length plus 1:
>>> (' ' * 100).count('')
101
That’s because empty strings are considered to exist between all the characters of a string; for a string length 2, there are 3 empty strings; one at the start, one between the two characters, and one at the end.
So yes, the results are different and they are entirely correct.