I see. Well in this case, we can be sure that the two-sample KS result is simply misleading -- i.e. wrong. That's because, at least at daily frequency, there is voluminous evidence that S&P500 returns are not normal: having skewness, excess kurtosis, and much heavier tails than a normal distribution. This is clear from both the sample moments, the mentioned Q-Q plots, and maximum likelihood fits to parameterized non-Gaussian distributions.

In fact, one knows from basic GARCH modelling that daily SPX returns are not even

conditionally normal, conditioning on the daily volatility estimates. Again, this is due to the relatively wide tails.

Apparently, the problem with the K-S test is that it is not sensitive to the tails. A bit of googling a few minutes ago confirmed the notion. See the

Abstract here:

It is well known that the Kolmogorov-Smirnov (K-S) test exhibits poor sensitivity to deviations from the hypothesized distribution that occur in the tails. A modified version of the K-S test is introduced that is more sensitive than the K-S test to deviations in the tails.

The bottom line is that K-S is apparently a very poor way to investigate deviations from normality for financial returns data. Your results are simply a case in point.