I think there is a difference in the approaches, given that the Chi-squared test statistic for the two-sample version is ~1.52, while for your one-sample version it is ~1.81. If group size doesn't matter and if you're justified in adding up successes as you have, I'd expect the test statistics to be nearly the same.

Edit: I'd expect them to be nearly the same since the Chi-squared distributions would be parameterized similarly, so if we have similar results, we should see similar test statistics. Maybe my reasoning here is incorrect though!