I don't think anyone claims it's /exactly/ the same entity (except in a legal sense after a government-in-exile is restored home, such as after World War II). But there's a general sense that a country can in some way be a continuation of a previous one, particularly if it shares the same language and a similar territory.
Compare the borders of something like the Duchy of Bohemia and the modern-day Czech Republic. That's two states over a thousand years apart, separated by centuries of highs and lows, including uncountable foreign invasions and Austrian rule for four centuries. And yet there's something obviously parallel to them - states ruled from Prague, inhabited largely by Czech speakers, extending to virtually the same territory.
Europe's natural and linguistic borders are relatively stable, so the emergence of similar states over similar territories in time is not unexpected.
Compare the borders of something like the Duchy of Bohemia and the modern-day Czech Republic. That's two states over a thousand years apart, separated by centuries of highs and lows, including uncountable foreign invasions and Austrian rule for four centuries. And yet there's something obviously parallel to them - states ruled from Prague, inhabited largely by Czech speakers, extending to virtually the same territory.
Europe's natural and linguistic borders are relatively stable, so the emergence of similar states over similar territories in time is not unexpected.