The important thing to understand is that you cannot directly compare labels in WSUS to labels in Patch Manager, because they are not equivalent.
In WSUS there are only four reportable states: Installed, Needed, NotApplicable, and Failed. The Needed state includes three substates: NotInstalled, Downloaded, and InstalledPendingReboot.
Patch Manager explicitly enumerates all six states: Installed, NotApplicable, Failed, Not Installed, Downloaded, and InstalledPendingReboot.
As such, Patch Manager does not provide a "Needed" column, so it will be necessary to clarify which column you're actually using.
To compare the WSUS "Needed" count, you'll need to calculate the SUM(NotInstalled, Downloaded, InstalledPendingReboot) in Patch Manager.