I have a negative confidence interval ((-35.346,-8.570) for an independent samples t-test.

I understand confidence intervals for the mean. However, I am uncertain about the interpretation of the confidence interval for a difference in means.

Is this an accurate interpretation? The confidence interval for mean difference in life satisfaction for the two groups is (-35.346,-8.570); as this interval does not contain zero, I can be confident that I have used a method that that will produce significantly different or unequal population means 95% of the time.

Or should I interpret the CI as follows: The confidence interval for mean difference in life satisfaction for the two groups is (-35.346,-8.570); as this interval does not contain zero, I can be 95% confident that the population means are significantly different or unequal.

Is this splitting hairs?