Confidence Interval - Revisit I've read in many articles about Confidence Interval as below
One such article link: https://www.statisticssolutions.com/misconceptions-about-confidence-intervals/

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*[FALSE] - There is a 95% chance that the true population mean falls within the confidence interval.


*[TRUE] - 95% of the confidence intervals calculated from these random samples will contain the true population mean.
Aren't both the statements the same?
Thought Process
We plan to take 100 sets of random samples. From the TRUE point 2, around 95 of those intervals (good set) will contain the True population mean while around 5 intervals (bad set) will not contain the mean.
For the first set, we got a confidence interval, say [c1_start, c1_end]. The chance of this confidence interval belonging to the good set is 95 out of 100, and if it's in this set, it'll contain the true population mean. Thus, there is 95% chance/probability that the confidence interval [c1_start, c1_end] will contain the true population mean which is the 1st statement.
How come then the first statement is considered FALSE? Which part of my thought process is incorrect?
Based on the excerpt from Introduction to Statistical Learning
The first point is True, or did I understand it wrong
A 95% confidence interval is defined as a range of values such that with 95% probability, the range will contain the true unknown value of the parameter
My other question is if Confidence Interval can only be explained if we do the experiments many-many times, what does a single confidence interval tells me?

I view this as a philosophical question with no uniformly satisfactory answer.
Consider a 95% CI for $\mu$ based on a random sample of size $n$ from $\mathsf{Norm}(\mu, \sigma),$ where $\sigma$ is known. Before data are observed, there agreement among frequentist statisticians that $$P\left(\frac{|\bar X - \mu|}{\sigma/\sqrt{n}} \le 1.96\right)= P\left(\bar X - 1.96\frac{\sigma}{\sqrt{n}} \le \mu \le \bar X + 1.96\frac{\sigma}{\sqrt{n}}\right) = 0.95.$$
However, after data are available, there is disagreement whether the above remains a true probability statement. One can argue that the word "confidence" (instead of "probability") came into use because it is sufficiently vague to avoid arguments. About all one can say for sure is that, over the long run, the procedure giving rise to the interval $\bar X \pm 1.96\frac{\sigma}{\sqrt{n}}$ will cover $\mu$ 95% of the time. References to what this interval means for the specific experiment at hand are bound to provoke unproductive arguments.
When frequentist statistical consultants tell clients that a given CI is "95% sure" to include the true value of value of $\mu,$ they can feel safe because the exact true value of $\mu$ is typically never known.
In a Bayesian context, a prior distribution established a probability framework. A Bayesian posterior probability (or 'credible') interval, based on the prior and likelihood function from data, can be taken as a true probability statement about the current data. If you believe the prior and the integrity of the likelihood, there can be no quibbling about the resulting probability statement about the posterior distribution.
