Q: Why does there appear to be a discrepancy in my Webcast Metrics stats when comparing to my live listener stats?

A: If you compare the chart and WCM you will see some discrepancies  and are the reason for that:

In WCM; the 'peak' displayed here is the highest AAS reached among the hourly reports that make up the report. So it's a 'highest hourly average listeners' which will be little lower than peak realtimes (because the peak realtime is momentary and that hour's average will always be lower than the peak). 

7 day chart; displays the stats as-of the top of the hour, every two hours. You won't see the actual peaks on that chart. 

90 day chart; this one is actually showing the peak realtimes and the time-of-day that the peaks were seen. Once you click on a staion to have the Detailed view, this chart will match the Detailed 'High'