Mathematically, the difference is that the equation 1/(1-S) will tell you that you need more material - which is probably true. I equate it to the industrial engineering problem of weighting time standards for efficiency, or even quality engineering's process yield. For example, if you have a process that produces 10% defective parts, you have to produce more than 110 parts to get 100 good ones. In fact, you have to produce 111.1: [ 1/(1-0.1) = 1/0.9 ]. It's sort of hard to explain over a post, but it is an important distinction. For small values of S, the difference is usually negligible, but it becomes much more significant as S increases.

Hope this helps! -Ben

The shrinkage formulas listed are for the outside (OD or wall) and the inside respectively. These are calcs used to figure out how much the part will shrink when it cools and hence you need to make the mold larger or smaller to accomodate.
You should talk to the foundry or whomever is processing your part about what percentage shrinkage they expect to see.

Agreeing with ecampos, you can also find some information from the Machery's Handbook which states that typ. contraction of castings in cooling are as follows: cast iron .0938 to .125 inch per foot etc etc etc steel is .1875 per foot. These shrinkage allowances are approximate values only because the exact allowance depends upon the size and shape of the casting and the resistance of the mold to normal contraction of the casting during cooling. Having worked in the Forging industry and now in Cold Header industry, shrinkage is a ratio obtained to some what closely from an operator of the machine - along with material bounce which you wouldn't have to worry about in injection molding nor casting.

dandrews@ferrycap.com