Hi,
for Windows updates, one or the other is possible automatically. You can find a summary of all possible scenarios and what policies to configure here:
https://learn.microsoft.com/en-us/archive/blogs/wsus/improving-dual-scan-on-1607
You can have both at the same time, but searches on WU/MU will need to be triggered by hand by clicking on the "Check online for updates" link in the Settings page.
HTH,
Andrei