After approving some needed updates, computers that are showing as needing the update don’t have it available to install when you run Windows Update. This is because, for an update to appear in WSUS as needed, WSUS must know about the update (from a synchronisation), whilst for the update to appear in Windows Update on the computer, the update must be both approved and downloaded.
If after approving an update in WSUS, it doesn’t appear in Windows Update on the computer, most likely you have set WSUS to download updates after they are approved, rather than when WSUS runs a synchronization. The update will then take a bit of time to appear in Windows Update because it has to be downloaded after it was approved.