The difference in US law falls under the Posse Comitatus Act[1] (which has been repeatedly expanded over the last 150 years): the government, by law, cannot use military forces for domestic law enforcement.
I'm no particular fan of the US military (much less the police), but the practical and historical distinctions between the two are substantial: one is the professional military of a country, and the other is a professionalization of antebellum slave catching posses.
I'm no particular fan of the US military (much less the police), but the practical and historical distinctions between the two are substantial: one is the professional military of a country, and the other is a professionalization of antebellum slave catching posses.
[1]: https://en.wikipedia.org/wiki/Posse_Comitatus_Act