der Neubau
new building
A newly constructed building that was completed only recently.
Unsere neuen Nachbarn sind in einen modernen Neubau am Stadtrand gezogen.
Our new neighbors moved into a modern new building on the outskirts of town.

new building
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new building
A newly constructed building that was completed only recently.
Unsere neuen Nachbarn sind in einen modernen Neubau am Stadtrand gezogen.
Our new neighbors moved into a modern new building on the outskirts of town.

The word 'Neubau' (new building / new construction) is a compound made up of the adjective 'neu' (new) and the noun 'der Bau' (construction, building). So it literally means a 'new building' or the 'new construction process'.
Die Firma plant einen Neubau für ihre Büros.
The company is planning a new building for its offices.
Pay attention to the preposition 'in' and the case. Movement toward a building is expressed with the accusative ('in einen Neubau' — into a new building), while a state or location requires the dative ('in einem Neubau' — in a new building).
Die Familie zieht nächste Woche in einen Neubau.
The family is moving into a new building next week.
You can often tell whether the building or the construction process is meant from the verb. Verbs like 'dauern' (to last), 'beginnen' (to begin), or 'planen' (to plan) refer to the process. Verbs like 'stehen' (to stand), 'sein' (to be), or 'wohnen in' (to live in) refer to the finished building.
Der Neubau des Bahnhofs dauert zwei Jahre.
The new construction of the train station will take two years.
building
'das Gebäude' and 'der Neubau' can both refer to a house or structure with walls and a roof. 'Gebäude' is the general word. It does not say whether something is old or new. 'Neubau' is more specific: it means either a newly constructed building or the process of constructing a new building. The words can be confused because every 'Neubau' can also be a 'Gebäude'. But not every 'Gebäude' is a 'Neubau'. If the age or the new construction is important, 'Neubau' fits. If you are speaking neutrally about a structure, use 'Gebäude'.

Im Neubau neben der Schule gibt es helle Wohnungen.
There are bright apartments in the new building next to the school.
Am Abend besichtigen wir das alte Gebäude neben dem Bahnhof.
In the evening, we visit the old building next to the train station.