aufgebaut
set up
Describes the state of having been erected, constructed, or assembled.
Das neue Regal war innerhalb von 30 Minuten komplett aufgebaut.
The new shelf was completely set up within 30 minutes.

set up / structured / built up
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set up
Describes the state of having been erected, constructed, or assembled.
Das neue Regal war innerhalb von 30 Minuten komplett aufgebaut.
The new shelf was completely set up within 30 minutes.

'Aufgebaut' (set up / structured / built up) is the past participle of the separable verb 'aufbauen' (to build up / to set up). It is very often used like an adjective to describe a state that is the result of building or setting something up.
Die Bühne für das Konzert ist bereits vollständig aufgebaut.
The stage for the concert is already fully set up.
In this meaning, 'aufgebaut' (set up) always refers to physical things that can be constructed or assembled. Typical objects are furniture, tents, scaffolding, or trade fair booths.
Das Zelt war schnell aufgebaut und bot Schutz vor dem Regen.
The tent was quickly set up and offered protection from the rain.
This meaning describes the organization of abstract things. You can recognize it from nouns such as 'Text' (text), 'Vortrag' (presentation), 'Argumentation' (argumentation), or 'System' (system), and adverbs such as 'logisch' (logically), 'klar' (clearly), or 'chronologisch' (chronologically).
Ihre Argumentation war sehr überzeugend und klar aufgebaut.
Her argumentation was very convincing and clearly structured.
When 'aufgebaut' (built up) describes an emotional state, it always refers to a person. It often appears in the phrase 'sich wieder aufgebaut fühlen' (to feel built up again) or is intensified by adverbs such as 'sichtlich' (visibly/clearly).
Nach dem netten Telefonat fühlte sie sich sofort wieder aufgebaut.
After the nice phone call, she immediately felt built up again.
organized
'organisiert' and 'aufgebaut' can both have something to do with order and structure. 'Organisiert' describes that something is well planned or prepared, or that a person is well organized. 'Aufgebaut' describes more how something is put together or structured, for example a text, a presentation, or a system. With a presentation, you may hear both words, but with a different focus: a well-organized presentation is well prepared and runs smoothly. A well-structured presentation has a clear structure with an introduction, main part, and conclusion. The risk of confusion comes from the fact that planning and structure often occur together.

Der Text ist klar aufgebaut, sodass man die Argumente gut versteht.
The text is clearly structured, so the arguments are easy to understand.
Der Workshop war gut organisiert, deshalb gab es kaum Wartezeiten.
The workshop was well organized, so there was hardly any waiting time.