The 'inheritance mechanism' is the -> operator,

No. The inheritance mechanism applies to method calls. Few of the -> operators have anything to do with methods. For example,

$x->[0]
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Furthermore, not all method calls use the -> operator. For example,

new Foo
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Forms of method calls:

$class->method(LIST)     # Static method call.
$object->method(LIST)    # Instance method call.
$x->Class::method(LIST)  # Pretend the LHS is class "Class".
$x->SUPER::method(LIST)  # Pretend the LHS is its super class.
method $x LIST;          # Indirect method syntax
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I think that's all of them.

Horse::speak("Horse") is a sub call. Subroutines aren't inherited. Subroutines don't have classes, so subroutines don't have parent classes, so subroutines have nothing from which they could inherit.

Thanks for the help. I think I'm getting a feel for it now.

class::method();

Is more like a name which is either defined or not.
There is no @class::ISA array search for "method".
There is no "automatic" first argument=class passed to the method.

class->method();

dereferences class for "method" and if not found will then use the "special method lookup mechanism" to search the classes listed in the @ISA array for "method"
The class name is automatically passed to "method" as the 1st argument.

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Fairly close?
Thanks again.

There is no @class::ISA array search for "method".

Correct, because you're not calling it as a method.

There is no "automatic" first argument=class passed to the method.

Correct, because you're not calling it as a method.

class->method(); dereferences class for "method"

Incorrect terminology, but yes. class->method() calls Class's method method, using inheritance if necessary.