Thre are center drills, 60 degrees inclusive, spoting drill 90 degrees inclusive and then either stubb drills ( short length ) and jobber drills.
The centering ones ( the ones with two tips ) are divided into straight profile ones such as the one in your link and the bell profile ones, the former is the one that you use for making the pilot hole prior to drilling, the later is for creating centers to be used in particular in offset turning between the two lathe centers as the sides of the resulting center hole will be curved. The one that looks like a short drill is actually to prepare the metal for spot welding or removing a weld ( I have never used one ) but you can use them to mark the center of a workpiece if you wish. Center drills also come in different sizes as you know ( use the one that is closest to you final intended dimension) and in different lengths to cater for some milling operations. Hope this helps.
I think the correct answer is use 60 degree center drills for drilling centers and spot drills for stating center holes for drilling. In my USAF training and I think in a lot of shops and text books 60 degree center drills are use for both drilling centers and starting holes.
I use mostly solid carbide 90 degree spotting drills; if you set the depth correctly your hole will have a nice chamfer when done.
This is directly from the McMaster Carr web site;
90° point angle bits are for centering and chamfering holes that will be followed by a smaller drill bit size. 120° point angle bits are for starting a hole that will be followed by a drill bit with a point angle from 90°-118°. 140° point angle bits are for starting a hole that will be followed by a drill bit with a point angle from 118°-135°.
I have wanted to try some of the higher angle drills in the CNC; the drill bits (not the spot drill) want to chatter a little entering the 90 degree spotted hole if the feed rate is up where it should be.
My Midge engine has 2mm countersunk holes in the back plate. My traditional countersink bits are quite large. Would 90 degree spotting drills be good for producing the countersinking on these small holes?