나라 is pure Korean and 국가 is Chinese. 나라 국(國) + 집 가(家) -> 국가 (國家). So if you read the new particles or watch the news, they'll use 국가 more often cuz it sounds more "official" I guess. For similar reasons, 국가 is used in all the legal terms as well. For example, international relations will be 국가 관계. In conversation, people use 나라 more often. For example, if you wanna say, "our country blah blah blah", you'll say 우리 나라 blah blah blah

It's kind of country(나라) nation(국가)