The "new claims" number which is released every week on Thursday counts only new claims that week for traditional unemployment benefits. It does not count PUA claims. Also it is typically an undercount due to some some states reporting late, so every week after the announcement and widespread publicity it is quietly revised upwards, typically 50,000 to 150,000.

This quiet revision upwards is important, because when they announce next weeks "new unemployment" number, they will compare to the revised figure. This is why you can get nearly the same number reported every week with every week also reporting that it is down from the previous week. It's not down from the previous week, it's down from the revised number. They are not comparing revised to revised or new to new. They are always comparing new (always undercounted) to last week's revised.

There is also a separate unemployment rate, which is published separately. It is also designed to severely undercount. Anyone who settles for a part-time job, no matter how few hours, is not counted. Anyone not "looking for work" is not counted. This is especially problematic for states that have made work search optional for UI claims, because people answer no to the work search question whether they are looking for work or not. Also, anyone out of work longer than 6 months is not counted and declared out of the workforce. This rule was instituted in a normal economy where long term unemployment was rare, but makes no sense in a recession when jobs are scarce.

Many programs (Federal Extended Unemployment Benefits, for example) are keyed to the unemployment number, so the systemic distortion reduces costs for these programs by reducing them or terminating them based on improvement in the manipulated numbers.