der Hase
hare
A mammal with long ears and strong hind legs that can run fast and is related to the rabbit.
Auf dem Feld saß ein großer Hase und putzte sich die Ohren.
A large hare was sitting in the field, cleaning its ears.

hare / bunny
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hare
A mammal with long ears and strong hind legs that can run fast and is related to the rabbit.
Auf dem Feld saß ein großer Hase und putzte sich die Ohren.
A large hare was sitting in the field, cleaning its ears.

The idiom 'wissen, wie der Hase läuft' is a fixed unit. It means that you understand a situation or know the usual procedures. The 'Hase' (hare) is not meant literally here.
Frag den neuen Kollegen nicht, er weiß noch nicht, wie der Hase hier läuft.
Don't ask the new colleague; he doesn't know how things work here yet.
As a pet name, 'Hase' (bunny/sweetheart) is very informal and is used only for people close to you, such as a partner or a child. It is often combined with a possessive pronoun like 'mein' (my).
Mein Hase, könntest du mir bitte helfen?
My sweetheart, could you please help me?
The 'Osterhase' (Easter Bunny) is a central figure in German Easter tradition. According to legend, he paints the eggs and hides them in the garden for the children.
Die Kinder können es kaum erwarten, dass der Osterhase kommt.
The children can hardly wait for the Easter Bunny to come.
Another common idiom is 'da liegt der Hase im Pfeffer'. It means that you have found the real reason or the actual difficulty behind a problem.
Das Geld fehlt, genau da liegt der Hase im Pfeffer!
The money is missing—that's exactly where the real problem lies!
darling / treasure
'Schatz' and 'Hase' can both be used as affectionate pet names for a person. 'Schatz' is very common and works for partners and children. 'Hase' is colloquial and often sounds more playful or cuter. The words can be confused because both occur in similar private situations. The difference is mainly in tone: 'Schatz' sounds more general and a little more neutrally affectionate, while 'Hase' sounds more familiar and playful.

Nach dem Essen fragt Tom: „Na, Hase, wollen wir noch spazieren gehen?“
After dinner, Tom asks, "Well, bunny, shall we go for a walk?"
Daniel nennt seine Frau oft Schatz, wenn er mit ihr telefoniert.
Daniel often calls his wife darling when he talks to her on the phone.