das Wunder
miracle
An extraordinary, inexplicable event that is often regarded as supernatural or divine.
Die plötzliche Genesung des Patienten grenzte an ein Wunder.
The patient's sudden recovery bordered on a miracle.

miracle / wonder
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miracle
An extraordinary, inexplicable event that is often regarded as supernatural or divine.
Die plötzliche Genesung des Patienten grenzte an ein Wunder.
The patient's sudden recovery bordered on a miracle.

The noun 'Wunder' is the root for many other words. These include the verb 'sich wundern' (to be surprised), the adjective 'wunderbar' (very good, fantastic), and the participle 'verwundert' (surprised/astonished).
Ich wundere mich, dass er schon wieder zu spät ist.
I am surprised that he is late again.
In the context of inexplicable events, 'Wunder' is often combined with certain verbs. Typical phrases are 'auf ein Wunder hoffen' (to hope for a miracle), 'an ein Wunder glauben' (to believe in a miracle), or when something 'an ein Wunder grenzt' (borders on a miracle).
Die Ärzte hatten die Hoffnung fast aufgegeben, aber die Familie glaubte fest an ein Wunder.
The doctors had almost given up hope, but the family firmly believed in a miracle.
To describe a surprising, fortunate fact, the structure 'Es ist ein Wunder, dass ...' (It is a miracle that ...) is often used. It is followed by a subordinate clause in which the verb comes at the end.
Es ist ein Wunder, dass du die Prüfung ohne Vorbereitung bestanden hast.
It is a miracle that you passed the exam without preparing.
The idiom 'sein blaues Wunder erleben' means to experience a nasty surprise. The word 'blaues' is a fixed part here, and the possessive pronoun (sein, dein, ihr, etc.) changes to match the person.
Wenn der Chef herausfindet, dass du gelogen hast, wirst du dein blaues Wunder erleben.
If the boss finds out that you lied, you'll be in for a nasty surprise.
surprise
'das Wunder' and 'die Überraschung' both have to do with something unexpected. A 'Überraschung' can be big or small: a gift, a piece of news, or an unexpected visit. A 'Wunder' is much stronger. You use it when something seems almost impossible, is inexplicable, or is especially amazing and fortunate. Learners may confuse the words because both describe something unexpected. As a practical rule: for normal unexpected things, 'Überraschung' fits better; for something very special or barely explainable, you are more likely to say 'Wunder'.

Nach dem schweren Unfall war es ein Wunder, dass niemand verletzt wurde.
After the serious accident, it was a miracle that no one was injured.
Zum Geburtstag wartete eine schöne Überraschung auf dem Küchentisch.
For the birthday, a lovely surprise was waiting on the kitchen table.