schlau
smart
Intelligent, clever, and able to understand situations quickly and find advantageous solutions.
Es war schlau von dir, die Tickets schon im Voraus zu buchen.
It was smart of you to book the tickets in advance.

smart / cunning
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smart
Intelligent, clever, and able to understand situations quickly and find advantageous solutions.
Es war schlau von dir, die Tickets schon im Voraus zu buchen.
It was smart of you to book the tickets in advance.

The meaning of 'schlau' (smart/cunning) depends on the context. If it refers to a clever, helpful idea, it is meant positively. If it describes an action that gives someone an advantage in a sly way, it has a slightly negative, crafty meaning.
Das war eine schlaue Antwort auf eine schwierige Frage.
That was a smart answer to a difficult question.
The expression 'aus jemandem/etwas schlau werden' (to make sense of someone/something) means to understand someone or something. It is almost always used in negative sentences or in questions and is fixed with the preposition 'aus'.
Ich werde aus diesem neuen Kollegen einfach nicht schlau.
I simply can't make sense of this new colleague.
In its positive meaning, 'schlau' (smart) is often connected with intellectual achievements or clever solutions. Typical combinations are 'eine schlaue Idee' (a smart idea), 'ein schlauer Plan' (a smart plan), or 'ein schlauer Kopf' (a smart person).
Sie gilt als schlauer Kopf und wird oft um Rat gefragt.
She is considered a smart person and is often asked for advice.
to understand
'verstehen' and 'schlau' both have to do with understanding, but they work differently. 'verstehen' is a verb and describes grasping the meaning of something. 'schlau' is usually an adjective and describes a person who is smart and quickly finds good solutions. There is a risk of confusion especially with the expression 'aus etwas schlau werden' (to make sense of something). It means something similar to 'etwas verstehen' (to understand something) and is often used in negative sentences. In a normal sentence, however, you say: 'Ich verstehe das Problem' (I understand the problem), not 'Ich bin das Problem schlau'.

Aus dieser Nachricht werde ich nicht schlau, weil wichtige Informationen fehlen.
I can't make sense of this message because important information is missing.
Nach der Erklärung versteht Tom die Aufgabe endlich.
After the explanation, Tom finally understands the task.