I think it's more of an industry vs. academia kind of thing. In the mid-90's before Java was released automatic memory management was mostly unknown to the unwashed masses. So garbage collection became synonymous to whatever Java was doing. However, The Garbage Collection Handbook originally published in 1996 defines garbage collection as: "All garbage collection schemes are based on one of four fundamental approaches; mark-sweep collection, copying collection, mark-compact collection or reference counting." So that's an example of terminology #2.

I think this is actually common in the literature, it has nothing to do with Wikipedia. Consider that Python is commonly described as a GC language, though it has always mostly relied on automatic reference counting to free objects (it does have a tracing GC as well to handle cycles, but I'm not sure if it always did).

Yep. The compiler generates code that works the same way that an experienced C programmer would hand optimise alloc/free calls and manually keep track of shared data by increasing/reducing a reference counter. There is no separate mark/sweep or whatever step.

I never understand why people refer to reference counting as garbage collection. It waters down the term so much it becomes essentially useless. Because under that assumptions basically every language has garbage collection in some shape or form.