der Gegenstand
object
A physical, material object or thing that you can see and touch.
Bitte räumen Sie alle persönlichen Gegenstände vom Tisch ab.
Please clear all personal objects from the table.

object / subject
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object
A physical, material object or thing that you can see and touch.
Bitte räumen Sie alle persönlichen Gegenstände vom Tisch ab.
Please clear all personal objects from the table.

'Gegenstand' (object / subject) is made up of 'gegen' (against / opposite) and the old word 'Stand' (from 'stehen' (to stand)). It literally describes something that 'stands opposite' you—whether a physical object in space or an abstract topic you are dealing with.
Ein seltsamer Gegenstand lag mitten auf der Straße.
A strange object was lying in the middle of the street.
The context tells you whether a physical object or an abstract topic is meant. If it is about touching, seeing, or moving, it is a thing. If it is about discussing, investigating, or learning, it is a topic.
Er nahm den glänzenden Gegenstand in die Hand.
He took the shiny object in his hand.
In the meaning of 'Thema' (topic), 'Gegenstand' (subject) is often combined with a genitive to specify the content. This construction is typical of formal written and technical language.
Gegenstand der Untersuchung war die Wasserqualität des Sees.
The subject of the investigation was the water quality of the lake.
As 'Thema' (topic), 'Gegenstand' (subject) is found in fixed expressions. Common ones are: 'Gegenstand der Debatte sein' (to be the subject of the debate), 'etwas zum Gegenstand haben' (to have something as its subject), or 'Gegenstand eines Vertrags sein' (to be the subject of a contract).
Die neuen Sicherheitsregeln waren Gegenstand einer langen Diskussion.
The new safety rules were the subject of a long discussion.
part
'der Teil' and 'der Gegenstand' can both stand for a thing that you mean or see. 'Gegenstand' is the neutral word for a material object that you can touch. 'Teil' can colloquially also mean 'Ding' (thing), but then it sounds more casual and often somewhat evaluative, for example surprised or impressed. For clear, factual situations, 'Gegenstand' is more natural. 'Teil' in this meaning is used more in everyday speech when you do not name exactly what the thing is.

Bitte legen Sie alle schweren Gegenstände in die untere Schublade.
Please put all heavy objects in the bottom drawer.
Was ist das denn für ein Teil auf dem Tisch?
What kind of thing is that on the table?