Confidence interval
The calculated interval has fixed endpoints, where μ might be in between (or not). Thus this event has probability either 0 or 1. We cannot say:  "with probability (1 − α), the parameter μ lies in the confidence interval." We only know that by repetition in 100(1 − α) % of the cases, μ will be in the calculated interval. In 100α % of the cases, however, it does not. And unfortunately we do not know in which of the cases this happens. That is why we say: "with confidence level 100(1 − α) %, μ lies in the confidence interval."