This could probably be worded better but:
Probability refers to using known population data to extrapolate towards a specific population. Here likelihood is more accurate since confidence intervals are making inferences about the true population, thus we cannot use the word probability in this case. (Ch2 pg 21)
The 95% refers to our confidence whereby if we were to repeat a study many times, 95% of those studies would include the true sample mean. One cannot say with certainty that the true mean is present within a confidence interval (Chapter 4 pg 35). Therefore a CI does not mean that we are 95% sure that the true mean is within our specific study.
Source: Other - Inuitive Biostatistics Harvey Motulsky
- Confidence interval is an inferred value for the population



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