the difference between the original steel and mild steel from percentage of carbon
As the first answers suggest, the prolbem is that these terms are not specific, they are not scientifically or technically defined. This is like asking: what is the difference between a four door car and a sedan? There are hundreds of steel alloys ranging from Fe + a little C + very little else to alloy and tool steels with significant amounts of Cr, Ni, Si, and a number of other elements + C. And... for any given steel alloy, there are many different ways to heat treat it. A given piece of steel can be heat treated so hard and brittle that it could shatter like glass and then it could be heat treated to make it into a spring or heat treated to make it stretch like taffy. If you really want to understand steels, yes, there are lots of books on sword making (some written by people who actually understand steels) but... you need to study metallurgy. There are graduate level courses just on the metallurgy of steels. Of course to understand this course you need to understand a whole lot of fundamental metallurgy. All this stuff on steel makes perfect sense because, in terms of weight (tonage) produced, steel is, hands down, nothing else remotely comes close, the most important metal humans have.
Carbon steel includes mild steel. Mild carbon steel(as it is referred to) contains .05 - .29% carbon. Medium carbon steel is from .30 - .59%. High carbon steel is from .60 - .99%. Ultra high carbon steel is from 1.00 - 2.00%. Steel is considered carbon steel up to 2.1%. Past that it is considered cast iron. The more carbon in the steel the harder and less ductile and maleable it is and also the more brittle it is. The less carbon in the steel more it will bend and shape without breaking. So in essence carbon adds strength but takes away from its elasticity. If you are interested in this subject an interesting source is swordmaking where hardness(carbon content) is crucial. The information behind this subject is pretty infinite.
