## what is a confidence interval?

From Wikipedia:

The confidence interval can be expressed in terms of a single sample: "There is a 90% probability that the calculated confidence interval from some future experiment encompasses the true value of the population parameter."

The confidence interval can be expressed in terms of samples (or repeated samples): "Were this procedure to be repeated on numerous samples, the fraction of calculated confidence intervals (which would differ for each sample) that encompass the true population parameter would tend toward 90%."[

A 95% confidence interval does not mean that for a given realized interval there is a 95% probability that the population parameter lies within the interval ... The 95% probability relates to the reliability of the estimation procedure, not to a specific calculated interval.

A confidence interval is not a definitive range of plausible values for the sample parameter, though it may be understood as an estimate of plausible values for the population parameter.

They seem like the same thing. What is the difference?