[atleta]

Well, I don't speak German (only recognize a few words), but the meanings of "Land" seem to include both "country" and "state". (As it's part of quite a few country names in German. Including Deutschland itself :) )

https://en.wiktionary.org/wiki/Land#German

[playing_colours]

“Deutschland” historically meant “the territory where German-speaking people live”, not a country. The name comes from early Middle Ages when the concept of a national country was not established yet. The idea of Deutschland as a country exists only from 19 century.

[atleta]

Well, that's true for most countries. The idea of nation states originated (or at least became popular) in the 19th century. Before that the areas were mostly organized around rulers (like kings).

But it has little to do with the current meaning of the word. I've looked up a few more countries that have the word 'Land' in their name: Weißrussland, England, Estland, Finnland, Griechenland, Russland, etc.

It indeed looks pretty common.