Alemán vs. germano
While both alemán and germano can translate to German in English, their usage in Spanish is quite different. Alemán is the common, everyday term for anything related to modern Germany, while germano is a more formal, historical, or specialized term.
Alemán
A1Alemán is the standard and most frequently used word. It refers to the people, language, and anything originating from the modern country of Germany. You would use this word in almost all everyday conversations.
Mi profesor de historia es alemán.
(My history teacher is German.)
Estoy aprendiendo a hablar alemán porque es un idioma fascinante.
(I am learning to speak German because it is a fascinating language.)
La cerveza alemana es famosa en todo el mundo.
(German beer is famous all over the world.)
Compramos un coche de fabricación alemana.
(We bought a German-made car.)
Muchos filósofos importantes eran de nacionalidad alemana.
(Many important philosophers were of German nationality.)
La reunificación alemana ocurrió en 1990.
(The German reunification occurred in 1990.)
Germano
B2Germano is a more formal, literary, or historical term. Its use is more specific, typically found in academic texts, journalism, or when referring to ancient peoples or language families. Using it in a casual context can sound pretentious.
El historiador estudia las antiguas tribus germanas que invadieron Roma.
(The historian studies the ancient Germanic tribes that invaded Rome.)
El inglés es una lengua germana, al igual que el sueco y el danés.
(English is a Germanic language, just like Swedish and Danish.)
El acuerdo comercial franco-germano fue un paso importante para la Unión Europea.
(The Franco-German trade agreement was an important step for the European Union.)
El Sacro Imperio Romano Germánico fue una entidad política compleja en Europa central.
(The Holy Roman Empire was a complex political entity in central Europe.)
El periódico hablaba sobre el nuevo canciller germano.
(The newspaper talked about the new German chancellor.)
La mitología germana está llena de dioses y héroes fascinantes.
(Germanic mythology is full of fascinating gods and heroes.)
Summary
In short, always use alemán for everyday references to modern Germany, its people, language, and products. Reserve germano for more specific and formal contexts, such as discussing a) the ancient Germanic tribes, b) the Germanic language family (which includes English), or c) in formal, often political or academic, writing about German relations (e.g., hispano-germano).