By the sounds of it you have got hold of some carbon tools from Tom & Dick's Cheapo Emporium, and I am sure they wouldn't have come from Tap & Die, as mentioned above.
The rough edges and burrs are a sort of giveaway sign of carbon screw cutting tooling. Very soft steel would be the hardest thing I would attempt to use them on. They normally cut OK, but tend to be very brittle in use and can easily snap, not just the taps, but dies as well.
A thing that I always found with cheap carbon sets I have used in the past, is the even with the die fully expanded (centre screw, tightened) the generated thread would still screw into the threaded hole, whereas normally, with good quality T & D's the male thread would be much too large to fit into the threaded hole, and so then you creep down in size until you get a perfect fit.
You would also most probably find that carbon taps are not serial, but all the same diameter in a set of 3. Good quality HSS have a smaller OD for first and second cut and a final larger OD for the plug (bottoming) tap. This allows for easier tapping to full size in tough or hard materials.
A lot of people don't realise that you can get serial taps, so when they only use say a second cut to thread a hole, the screws are either tight going in or sometimes lock up solid as they are screwed in because the threaded hole is in fact too small.
Arc Euro do some good general purpose serial taps at very reasonable prices for a set, and I have some in my collection, but never having used them on a real tough stuff, I can't comment on their life expectancy.
http://www.arceurotrade.co.uk/Catalogue/Cutting-Tools/TapsBogs
