The canonical text on garbage collection by probably the most respected person in the field considers reference counting (automatic or otherwise) to be GC (http://gchandbook.org/contents.html). I know that's appealing to authority, but what else can you use to prove the definition of a term? Also see [1], which argues these algorithms are all the same thing anyway.
[1] D. F. Bacon, P. Cheng, and V. T. Rajan, “A Unified Theory of Garbage Collection,” presented at the Proceedings of the 19th Conference on Object-Oriented Programming, Systems, Languages & Applications (OOPSLA), 2004.
While we can acknowledge that the more expansive definition of "garbage collection" includes ARC, we can still simultaneously hold another definition of "gc" to not include ARC when discussing Apple & Swift. That's the way Apple documentation and most others are using that term.
Apple docs:
"Garbage collection is deprecated in OS X Mountain Lion v10.8, and will be removed in a future version of OS X. Automatic Reference Counting is the recommended replacement technology."[1]
If we don't use the more common understanding of gc, Apple's documentation doesn't make sense. If we do a substitution of Apple's verbage using ARC==GC, we get nonsense such as:
"Garbage collection (which includes ARC) is deprecated in OS X Mountain Lion v10.8, and will be removed in a future version of OS X. Automatic Reference Counting (which is also part of garbage collection) is the recommended replacement technology."
With the insistence on ARC==GC, we'd have to parse that sentence as garbage collection is being removed and replaced with garbage collection.
It would be nice if we not redefine the meaning of computer terms that have be understood for decades. I know it's semantics, but I take the definitions I learned 20 years ago in my college comp-sci textbooks as the agreed upon definition.
Others would take the definitions They learned 10 or 50 years ago in their college comp-sci textbooks as the agreed upon definition, and those differ.
For example, what I learned decades ago doesn't include that 2004 paper that convincingly shows reference counting to be one end of a scale that has pure GC at the other end.
Yet, that paper made me realize that reference counting is, in some sense, garbage collection.
On the other hand, I see no big problem in having an ambiguous term. That happen all over the world, also in science. Chemists have 'alcohol' (ethanol) vs 'an alcohol' (a family of compounds that includes ethanol), mathematicians have words such as 'algebra', biologists have roses as a family of plants and as a subset thereof, etc.
[1] D. F. Bacon, P. Cheng, and V. T. Rajan, “A Unified Theory of Garbage Collection,” presented at the Proceedings of the 19th Conference on Object-Oriented Programming, Systems, Languages & Applications (OOPSLA), 2004.