This is completely different.

The is the politicians not being able to form a coalition. Imagine your congress not agreeing to fill some commissions or confirm some positions in government.

It is a 'shutdown' of the legislative branch, not the executive.

Not really comparable because the bureaucratic system kept running. It's just a completely different political system and "there is no government" means a different thing. US-style "government shutdowns" don't really happen in Belgium.