grau
gray
The color that is a mixture of black and white.
Der Himmel war heute von morgens bis abends grau und bewölkt.
The sky was gray and cloudy today from morning to evening.

gray
Loading your saved state.
gray
The color that is a mixture of black and white.
Der Himmel war heute von morgens bis abends grau und bewölkt.
The sky was gray and cloudy today from morning to evening.

The meaning of 'grau' (gray) depends strongly on the noun it describes. A 'grauer Himmel' (gray sky) refers to the color, while a 'grauer Alltag' (gray everyday life) describes a bleak mood.
Ich mag meinen neuen grauen Mantel sehr.
I really like my new gray coat.
In a figurative meaning, 'grau' (gray) often describes something monotonous, boring, or joyless. A 'graue Maus' (gray mouse), for example, is an inconspicuous, shy person.
Das Leben in der kleinen Stadt war ihm zu grau und ereignislos.
Life in the small town was too gray and uneventful for him.
When referring to people, 'grau' (gray) almost always describes hair color in old age. The expression 'grau werden' (to go gray) means that the hair loses its natural color.
Mein Vater ist stolz auf seine grauen Haare.
My father is proud of his gray hair.
In the context of laws or rules, 'grau' (gray) describes an unclear, not clearly defined area. Typical combinations are 'Grauzone' (gray area) or 'grauer Markt' (gray market).
Der Handel mit diesen Produkten bewegt sich in einer rechtlichen Grauzone.
Trade in these products takes place in a legal gray area.
'Graue Theorie' (gray theory) is a fixed expression for ideas that are very abstract and far removed from real life. It is often used as the opposite of practical application ('Praxis').
Das ist doch alles nur graue Theorie, das funktioniert im echten Leben nie.
That's all just gray theory; it would never work in real life.
white
'weiß' and 'grau' both describe light colors, so in some situations they can seem similar. 'weiß' is the very light color like snow or milk. 'grau' is between black and white and often seems somewhat darker or duller. For hair, people often say 'grau' when someone gets older, even if individual hairs look almost white. Learners may confuse the words because light-colored objects, clouds, or hair are not always clearly only white or gray. If something is truly light and has no dark tone, 'weiß' fits. If there is a dark or mixed tone, 'grau' fits better.

Nach vielen Jahren sind die Haare meines Vaters grau geworden.
After many years, my father's hair has turned gray.
Für die Feier zieht Anna ein weißes Kleid an.
Anna is wearing a white dress for the celebration.