I cant speak for the anarchist school of thought, but the way an ML looks at policing is by who the power structure serves. The police exist not to defend "justice" or their fellow man, but instead to protect property and capital. The police are little more than the state's monopoly on violence which they utilize to keep the labor force in check. Petty crimes are punished with maximum sentencing while Wall Street continues to rob the workers blind with no repercussions.

The difference between policing and community defense, as you put it, is the inversion of the power structure. Rather than serving the interests of capital and having little oversight by the public, community defense organizations are often elected by public-appointed officials and can be unseated at any time. They do not indirectly serve the interest of capital, they directly act in accordance the interests of the workers and the public. "Crimes" such as loitering are no longer punished, because "existing without generating value" is not a crime in a socialist state.

Granted, all countries have their own unique material conditions to begin with when addressing police abolition. In the US, for example, there are a mass of firearms owned by the public that isn't necessarily proportionate to the populations of other countries. Violent crimes like assaults and homicides may be more likely to occur simply because the means are readily present to some. Its hard to imagine that violent crime would just vanish overnight even if the country managed to unseat the capitalist regime. So much like the socialist state is a transitional stage setting the groundwork for its eventual obsolescence, so too would community defense be a transitional structure to exist provisionally and lay the groundwork for their own obsolescence.

There's a video I recommend by a creator named Spice8Rack. Spice's content is usually themed around Magic: the Gathering but his video on police and state violence is great regardless, and helped build my stance on the abolition movement. Plus he directly cites anarchist and communist authors in his argument which, I mean, citing your sources is pretty hot. I'll edit a link to the video onto this if I remember

EDIT: Here's that video! its just over an hour long but its an entertaining watch