Oh good! I'm glad to know that I didn't get the "wrong" center drills since my primary application is indeed starting holes on the lathe (or maybe in the mill). I guess I'm still a little confused about the purpose or point of the spotting drill, but I think this might be in definition alone. If I had to take a guess at what "spotting" a hole means, I'd imagine it meant to start the hole in the correct location. IF that's true, one could claim (maybe?) that a center drill is a specialized type of spotting drill since it is also used for starting the hole in the correct location, namely- the center of spinning stock. Am I on track here?
If all that's true, then I'd infer that a center drill is for starting a hole specifically on a lathe, and a spotting drill is for starting a hole everywhere else. Yes?
Unless you are in a production environment any method of spotting a hole is valid, there is no right or wrong way there is only a faster or slower way.
Let us use a bit, no pun intended, of reason, lathe centers are typically 60 degrees so a Center drill is 60 degrees with a pilot diameter that ensures that the sharp point of the center does not reach the bottom of the hole. When spotting a drill location the pilot diameter is not in any way useful. A center drill is used to create work holding features.
Why do many taps have centers in each end? They are not there to make your life easier, they are there because this is how the manufacturer holds them, small taps are often sharply pointed ends where the point is held with an external center when being ground.
Spotting drills are often 90 degrees included angle which will create a 45 Degree chamfer on the hole entrance which will require no deburring afterwards, this in itself is an advantage.
They are less easily broken then center drills.
The angles are better when followed by a twist drill, this may help answer your original question. As a hobbyist are you drilling 10 holes per day or 1000 holes per day?
If only several holes per project use whatever method works for you and your equipment as this is what is the "right" method. Ignore most of the "How To Do This Correctly" web advice, for many people the exercise of thinking about a process is more important then actually doing it.