There are several different 'flavours' of self-tapping screws available, each designed for different purposes.
Some 'self tappers' just have a spire point which deforms the metal to follow the thread. IMO not really 'self tapping' more 'self forming', as they
deform the metal rather than cut it. They are good for fixing thin sheet metal.
Some have flutes cut into their threads, so they can
cut a thread as you wind them in. They are 'proper' self tapping screws, good for fixing into thicker steel sections.
There are self drilling fasteners. The tip is formed into a drill point to cut the correct size hole and the threads are fluted to cut a thread.
They drill their own hole, thread it and secure themselves in place in one operation - great when you've got a lot of fixings to put in.
You really do need the correct size hole, down to the last tenth, or even hundredth of a millimetre to use self tapping screws efficiently. Tool suppliers usually stock a more extensive range of bit sizes than DIY stores, including imperial, letter and number sizes, so you can select a drill bit size down to within a few thousanths of a mm of the size you want by using tables like
http://www.tapdie.com/html/mm_equivalent_inch__no__letter.html You will see there are something like 25 different size drill bits available within the range of 4mm to 5mm diameter.
I agree with the comments about using a lubricant. A bit of lard on the screw points works surprisingly well.
I have no problems using a good quality carbon steel tap to thread the right size hole, using appropriate lubrication, but I agree HSS taps are more forgiving in terms of tapping hole sizes and lubrication.