next to each other / side by side
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side by side
Spatially directly at the side of something or someone; side by side.
Im Regal stehen die deutschen und die englischen Bücher nebeneinander.
On the shelf, the German and English books are standing side by side.
'Nebeneinander' (next to each other/side by side) is a compound made up of the preposition 'neben' (next to) and the reciprocal pronoun 'einander' (each other). So it literally means 'next to the other one'.
Die beiden Kinder saßen still nebeneinander auf der Bank.
The two children sat quietly side by side on the bench.
As an adverb, 'nebeneinander' can appear in different positions in the sentence. It can be in position 1 to emphasize the arrangement, or after the conjugated verb.
Nebeneinander wirkten die beiden Häuser sehr unterschiedlich.
Side by side, the two houses looked very different.
When 'nebeneinander' is used with abstract nouns like 'Projekte' (projects), 'Aufgaben' (tasks), or 'Systeme' (systems), it usually means 'at the same time' or 'in parallel'.
In unserem Unternehmen existieren alte und neue Softwaresysteme nebeneinander.
In our company, old and new software systems exist in parallel.
The phrase 'nebeneinander her leben' (to live side by side) is a fixed expression. It describes couples or partners who live together but no longer have an emotional connection or shared interests.
Nach zwanzig Jahren Ehe lebten sie nur noch nebeneinander her.
After twenty years of marriage, they only lived side by side.
together
'zusammen' and 'nebeneinander' can both describe people or things not being separate. However, 'zusammen' emphasizes doing something together: people do something jointly or belong to a group. 'nebeneinander' mainly describes position: two people or things are side by side. It can also mean that two things are happening at the same time without really being connected. Learners may confuse the words when people are in the same place. If the shared action is important, 'zusammen' sounds more natural. If the position is important, 'nebeneinander' fits better.
Im Bus saßen du und Max nebeneinander, aber ihr habt kaum gesprochen.
On the bus, you and Max sat next to each other, but you hardly spoke.
Die Lehrerin arbeitet heute zusammen mit den Schülern in der Werkstatt.
The teacher is working together with the students in the workshop today.