When we use cycle time, it is in calendar days. For example, when we say we have a cycle time of 15 days, it means two full calendar weeks, including weekends.
We use calendar days to talk in a customer perspective. This comes from Lean thinking. When a customer ask when will it be done, he wants to be answered in elapsed time/date.
This is different than using "time spent" duration. Calendar days includes delays, time of meetings, interruptions, downtime, etc. It is more reflective of the effectiveness of your workflow, and it is more accurate when we want to forecast delivery dates for example.
One common fear is that including weekends and holidays screw the metrics. Over the time, the numbers will even out. And we advocate for continuous delivery, making smaller batches and reducing WIP. The results will be less items that carry over multiple weeks.