I'll take a stab at it; perhaps others will offer corrections or more details.

Steel alloys have properties (strength, hardness, mallebility, weldability) that vary considerably depending on the composition of the alloy, heat treating, whether it's air hardening, etc.

There are SAE-AISI standard designations for alloys like 1020 carbon steel and 4130 Chromium Molybdenum (see http://www.materialsengineer.com/E-Alloying-Steels.htm), and there are manufacturer's designations like Reynolds' 531, 631, 753, 853, 953, and Columbus SL, SP, SLX, Life, Genius, MAX, Spirit, Zona, Brain, and XCr. Some alloys, like Reynolds 531, are Manganese Molybdenum rather than Chromium Molybdenum.

Some of the heat treated steels lose strength at the joints if the joints are heated too much during the joining process, while newer air hardening steels actually become stronger at the joints with higher heat. For this reason, frames built using heat treated steels like Reynolds 753 are usually built using lugs and silver brazing rather than welding, and air hardening steels like Reynolds 853 can be TIG welded without too much concern that the heat used in joining the tubes will weaken the steel.

All steels have roughly the same density and elasticity, but the strength of different alloys varies significantly. So, stronger alloys can have tubing with thinner walls which makes frames that weigh less. But because the thinner walls are more flexible (remember, all steels have the same modulus of elasticity), oversized tubes with larger diameters make up for the loss of stiffness inherent in the thinner walled tubes.

Most bicycle tubing today is "butted", which means the walls are thicker at the ends - where most of the stress is concentrated - than in the middle. Double-butted means both ends are thicker than the middle section, while single-butted means only one end is thicker. Typically, seat tubes are single-butted with the butted (thicker) end at the bottom bracket and the thinner end at the seatpost end.

Some lower end frames are built with plain, straight gauge carbon steel. Because carbon steels like 1020 don't have the strength of more sophisticated alloys, the tubes are not usually butted, and therefore the frames are heavier.

The tubing manufacuturers have websites that usually describe their tube sets, including the alloy used, lengths and outside diameters of the various tubes, and the butting profiles of the tubes, along with characteristics of the alloy like ultimate tensile strength.

Hope this helps.