The second part is a huge differentiator from "normal" military. A police force even if administratively under the military has one crucial differentiator: their daily duties and training revolve almost exclusively around policing civilians from the same country. Military training and tactics are overwhelmingly aimed at dealing with foreign enemy combatants, mainly other military forces.
The methods give away the intentions and expected outcome. The US already has a very "militarized" police force. You send actual military only if you want to inflict the maximum amount of damage, and with that threat overwhelmingly scare the country into compliance.
That is the part that is not universally true. There are plenty of Gendarmeries who are soldiers first, with combat training and ethos, who also perform policing duties, the Marechaussee included.
Fair enough, but Wikipedia confirms that they all have civilian law enforcement and police duties so clearly their training, tactics, and experience revolve heavily around dealing with civilians.
I'll still take that over "soldiers only", even more with US's very active military where the soldiers routinely see active combat. Both the theory and practice shapes their "soldier vs. enemy combatant" world view. That's a hammer if I've ever seen one.
* when used domestically, it's under the Minister of Justice and Security
* there's also no Dutch equivalent of the U.S. presidency with unilateral executive control over the military
I'd argue this kind of danger is something you get more in presidential systems. Not that we all shouldn't be wary of military forces within our civilian populations.
In the Netherlands, the Royal Marechaussee are literal soldiers who perform military police duties and also many civilian policing duties, but all of them are soldiers first.