Basic Examples (3) 

Two expressions that are identical are considered SameQ:

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However, they are different instances of the same data:

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By contrast, the value for c in the below is literally the same value for a, since both reference the same memory location:

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Scope (1) 

SameInstanceQ can accept any number of arguments:

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Properties and Relations (5) 

SameInstanceQ always returns True for a single argument:

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Compare to SameQ:

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SameInstanceQ[] is defined to be True:

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This matches the behavior of SameQ:

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Memory is typically allocated for each new expression that is created, even if it shares the same value as an existing expression:

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In this case, a and b have identical values:

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However, their values are stored separately in memory, since each expression was created separately:

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Reusing expressions that are already created can save memory:

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The value for a is literally the same value for b, since both reference the same memory location:

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Many simple expressions are already preallocated in the kernel:

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These are not necessarily atomic values:

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Atomic expressions that are SameQ are not necessarily SameInstanceQ:

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Possible Issues (2) 

Having all of the corresponding parts of expressions be SameInstanceQ does not imply the parent expressions are SameInstanceQ:

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Small integers are already created in memory, so they are always the same instance:

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Larger integers are created as needed:

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Find the range of small integers that are preallocated in memory:

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Neat Examples (1) 

Test modifications on expressions to see which lead to new instances:

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