Let me try out a few definitions for size. A “nation” is people who are bound together by ties of blood, language, or culture. A “state” is an area of land with a population, borders, and a government. When most of the people who live within a state belong to the same nation we call it a “nation-state”. Between the wars Germans were a nation, Germany was a state, but Germany was not a nation-state. One of the factors behind World War II was the tension between nation and state with respect to Germans.
An “empire” is a state governed by a monarch (any autocrat, really) that rules over more than a single nation. Multiple nations that are governed by the same republic are either colonies or the same republic.
When multiple ethnic groups live in the same state with no one ethnic group comprising the overwhelming preponderance we think of it as “pluralistic”, especially if the various ethnic groups are tolerated. It’s a matter of degree. Most states are pluralistic. Estonia is pluralistic (70% ethnic Estonian). The Republic of Ireland is a nation-state (90% or more Irish). Hungary probably qualifies as a nation-state.
Disagreements? Modifications? Extensions?