Reynolds 631 is a manganese-molybdenum while 4130 is a chromium-molybdenum. Reynolds 631 is air hardened and gets much stronger after cooling as a result.

531 is basically the same as 4130. 631 is an improved version of 531, so it's probably not much better than 4130. At least not enough to base a purchase decision on. Reynolds 531 is not 4130, and Reynolds 631 is DEFINITELY not 4130. Reynolds brand names (531, 631, 853, 753, etc.) all refer to both a specific model of tubings, and the specific materials used to make them. Some are available in a variety of thicknesses and butting, and some are not. They are brand names.

4130 is a specific composition of steel, often simply referred to as "chomoly". It is made into tubing by a number of manufacturers in just about any thickness, butting, etc. that you can think of.