How is this distinct from dual core computing? If the basic processor core has one each of ALU, fetch/decode unit, and execution context, then are simultaneous multi-threading processors basically equivalent to dual-core computing?

I suppose this is all on the same chip, so maybe it has memory benefits (they share the closest caches, so latency and bandwidth for that small amount of memory would be improved perhaps). Are there certain applications where this would be preferred over a standard dual core setup?

Perhaps, in addition to the memory benefits, there is the benefit of getting increased compute resources by just adding ALUs instead of having to duplicate other units in a separate core. You also could possibly have the option to exploit ILP if it exists with this setup.