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Let me know if I'm incorrect here.

When I press AltD I create an instance of an object. My triangle count don't change though.

When I press ShiftD I create a duplicate of an object. Triangle count goes up.

When I create an array modifier, are the cloned objects instances, or duplicates?

If so, how do I use the array modifier to produce duplicates without producing additional geometry?

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When I press alt + D, I create an instance of an object. My triangle count don't change though.

Incorrect! You don't create an instance, though you have the right to mean something different by the word instance - still, AltD is an operator that creates a new object wrapper for the mesh (in your case). It is a linked copy, everything is linked to the same data as the original object, including its mesh (so it makes some sense to call it an instance of the mesh, but not the object). The triangle count of all your meshes doesn't increase, because you didn't create a new mesh, but the displayed triangle count of course does increase.

When I press shift + D, I create a duplicate of an object. Triangle count goes up.

Correct! You Duplicate the object, which also duplicates a mesh associated with this object.

When I create an array modifier, are the cloned objects instances, or duplicates?

Neither. The Array Modifier doesn't duplicate your object as if you pressed AltD or ShiftD in Object Mode. Instead, it duplicates it as if you pressed ShiftD in Edit Mode. You don't produce new meshes or objects this way, you also don't modify the Mesh data until you apply the modifier.

If so, how do I use the array modifier to produce duplicates without producing additional geometry?

You can't. You can use Geometry Nodes instead, or Instancing (first link) - basically, instead of using an array on your object, use it on a single vertex or a plane, and then set that vertex/plane object to be an instancer, and parent your object to that instancer. If you don't want to actually use instances, you can then (even without applying the Array modifier) select the instancer, F3 Make Instances Real. This will produces deep-linked objects using a single mesh (as if you used AltD)

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When you create the modifier, but have not applied it, there is only one object. That object contains multiple duplicate copies of the original mesh, and you can only edit that mesh.

When you then apply the modifier, there is still only one object but the individual meshes are no longer duplicates, they are each individual meshes that can be edited separately.

When you then separate the object by loose parts, you have N individual objects, each with its own mesh. They are not duplicates of each other. Note: If the original mesh had separate islands, like Suzanne's eyes, mentioned in a comment, then each island becomes a new object, so you lose that grouping as well.

You can make the new objects all have duplicate meshes of the original by selecting all of the objects, choosing the original last, and they typing CtrlL and selecting link object data from the popup menu, but this will move all of the duplicates to the same coordinate as the original and you will have to move them apart again.

There isn't a method to relink the meshes without moving the copies.

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  • $\begingroup$ relink the meshes without moving the copies - the missing step is to press F3 and type set origin to geometry, but this only really works if the original geometry had its origin in the center of mass... Also, Separating by lose geometry won't work for Suzanne, as 🐵 has unconnected eyes. You could use a trick with geonodes like so i.imgur.com/aMzxfXf.png to then separate by material, but obviously it's problematic if you want to use some materials...But then again if you Ctrl+L to link the data back to the original, it doesn't matter... $\endgroup$ Feb 15 at 22:01
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    $\begingroup$ Yes, I oversimplified, ignoring objects that were originally multiple meshes. Updated to note that $\endgroup$ Feb 15 at 22:21

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