There's a whole confusion around the whole terminology regarding the social order and its shapes, there's almost no match, which frustrates the translators since forever, because the US is so different from Europe.

The local terms:

država (the federal entity) - should be called state, whose members were republics, exactly opposite from the american, where the members were states and the federation is a republic

država (as authority) - doesn't exist in the US, specially not as an adjective. „To je državno“ (that is of state) means it's not private nor public property but something belonging to the overall apparatus, regardless of level; in the US, it'd be called government[al], but here it also applies to municipality or province or city level. „Državni posao“ - gov't job - is when one's employed in the system at any level.

republika - a type of state, not the federation; in the times of SFRY, one of member states. „Republički nivo“ - state level.

vlast - authority, power, rule. Can't be translated as „law“ or „enforcement“ because these are just segments of it. One is „na vlasti“ when in power.

vlada - the government, but this means only the PM and other ministers. As an adjective, it's very narrow, pertains to „vladino saopštenje“ (govt's announcement) and such, the other meanings are covered by „državni“ (of the država).

American terms:

State (država) - the fifty, but then the state as an adjective doesn't mean as above, it means „state level“, below federal, above city/county.

Country (zemlja) - one of the couple of hundred on Earth

Government (vlada) - again different from here, it's the president and department secretaries, no prime minister, and the accompanying agencies. There are ministers with their ministries - of foreign or domestic affair, economics (not economy, since about 2003. the engrbian language introduced this confusion at the gov't level).

Authority - not same as vlast, because it mens authorization first („under whose authority“); in plural, it's various authorities per sector - education, transportation, postal, military (which is not one, there are four of them), law enforcement etc etc. Not as unified as here.

Republic - Serbia was one of the member republics in SFRY, now it's Republika Srbija (often mistranslated as „Republic of Serbia“ - wrong, it doesn't have a republic, it is one).