ausgezeichnet
excellent
Describes something as excellent, outstanding, or of very high quality.
Das Essen im neuen Restaurant war wirklich ausgezeichnet.
The food at the new restaurant was truly excellent.

excellent / awarded
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excellent
Describes something as excellent, outstanding, or of very high quality.
Das Essen im neuen Restaurant war wirklich ausgezeichnet.
The food at the new restaurant was truly excellent.

'Ausgezeichnet' (excellent / awarded) is the past participle of the verb 'auszeichnen' (to distinguish / award). 'Auszeichnen' means to single out something or someone as special, either through an honor or because of high quality. The adjective also has this double meaning.
Er ist ein für seine Romane ausgezeichneter Autor.
He is an author awarded for his novels.
In the meaning 'excellent', 'ausgezeichnet' (excellent) often stands alone after a verb. In the meaning 'honored/awarded', it usually stands directly before a noun, often followed by an explanation with 'für' (for) or 'mit' (with).
Der Service in diesem Hotel ist ausgezeichnet.
The service in this hotel is excellent.
As a synonym for 'sehr gut' (very good), 'ausgezeichnet' (excellent) is a strong and somewhat elevated expression. It gives special weight to a positive evaluation.
Ihre Präsentation war nicht nur gut, sie war ausgezeichnet.
Her presentation was not just good; it was excellent.
When 'ausgezeichnet' means 'honored' or 'awarded', you often find a preposition such as 'mit' (with), e.g. 'mit einem Preis' (with a prize), or 'für' (for), e.g. 'für seine Verdienste' (for his services/achievements), which describes the honor more precisely.
Die Forscherin wurde für ihre Entdeckungen mit dem Nobelpreis ausgezeichnet.
The researcher was awarded the Nobel Prize for her discoveries.
good
'gut' and 'ausgezeichnet' can both describe high quality. 'gut' is more general and fits almost any everyday situation. 'ausgezeichnet' is much stronger and sounds like high praise. You use it when something is truly very good, for example a result, a meal, or a piece of work. In this meaning, it is not about an official award, but about quality. As a simple rule: 'gut' is positive; 'ausgezeichnet' is very positive.

Das Team bekommt viel Lob, weil die Arbeit ausgezeichnet ist.
The team is getting a lot of praise because the work is excellent.
Im Gespräch hat Frau Hoffmann eine gute Lösung vorgeschlagen.
In the discussion, Ms. Hoffmann suggested a good solution.