SD is only the average length of the bullet, without regard for caliber or bullet shape. I know this sounds incorrect because SD has been used as the holy grail for estimating a bullets ability to penetrate and other characteristics. If you disagree, just look at the calculation: bullet weight divided by quantity diameter x diameter. Since bullets are round and diameter x diameter would give the area for a square bullet, the SD function gives a proportionate number to the other option: bullet weight divided by bullet area (cross-section). So if bullets were cylindrical and had the same density, then all bullets of all calibers with the same SD would be the same length. A .224" bullet with an SD of .250 would be the same length as a .308" as a .458". Although they would be the same length, their shapes would be entirely different. The .224" bullet will be very long relative to its diameter, while the .458" will be very short relative to its diameter.
In terms of penetration, the bullet is slowed by stuff getting in the bullets way which is to say that the .458" bullet has more surface area to contact more stuff than the .224" bullet. If bullets were non-expanding so the formula was kept simple, the smaller diameter bullet would penetrate farther than the larger diameter.
So the solution to penetration (keeping strictly to the shape issue, bullet construction is separate) is the ratio of bullet weight to diameter. Based on the experiences of several hunters and their printed comments regarding what bullets worked well for them, it appears that a ratio of what would be termed "three calibers" is a good starting point. That is to say, the bullet will average three times longer than its diameter. The actual bullet will be slightly longer than the three calibers because the rounded point extends its average length. To achieve the three calibers measure, as the bullet diameter is increased, the SD will also noted to increase. For example, a .375" bullet with 3 calibers will have a much smaller SD than a .458" bullet but there are examples of bullets that will have similar penetration.
That's a long way of saying, SD is only a guideline when seeking penetration potential. Bullet weight and frontal area as well as construction, velocity and spin are also factors to consider.