From memory - 4130 is the number given to "steel" that conforms to some engineering US standards. It is a steel with very small % of chromium, smaller still of molydbendum, and a couple of other additions to make a stringer "alloy". International manufacturers like True Temper, Tange, Columbus will use this number as the description for their steels produced to these defined laid down formulas.
501 and 531 are specific numbers used by Reynolds tubing to describe their own chemical compositions for tubing they make. Its largely the same stuff. Steel tubing with added metals to make alloys. 501 is closest to 4130. 531 is a diffenernt formula. I think Reynolds add a metal (or some element) which actually "air hardens" the tubing when welded, where as straight 4130 softens and weakens under very hot (welding) tempratures. Reynolds I imagine, hold patents for their tubing, which is why no one else uses their designations.
Technically, 531 was used for race bikes, it could be drawn and made thinner walled than 4130 from other manufactuers. 501 I think was better used for the thicker walled applications of BMX bikes.
Worth googling, this is all from 25 year old memory.
Edit -
531 is a "managanese molybdenum". So its got added manganese to the steel. This is what makes it for "racing bike" applications better.
Then you get later tubing from Reynolds like 555 which is very similar to 501, and 853 which is an improved vertsion of 531.
Given that 531 and 501 have existed since the 1030's, its no suprose that modern chemistry has found improvements that lift the performance of 501/531 to an extent that a new number is appropiate.
The other thing to watch is that frames branded "501" or "531" may still be like our Diamond Back Silver Streaks or Mongoose Californians, and have a main tube, or front triangle of the "elite" metal, with mild/hi ten rear ends.
And as important, 4130 and 501/531 can still be single or double butted - a single butted 531 drawntube may be as heavy as 501 double butted - so the "quality" of the tube set is as important as its chemical make up.
