These socks should be identical, were it not for gauge. They were knit with the same pattern*, same yarn and same needles, but by two different knitters. I'm a continental knitter (picker), while Mom, who taught me to knit, is an English-style knitter (thrower). Her stitches are tighter than average, whereas mine are looser than average. The result? Her sock, with a gauge of 5.5 stitches per inch, would fit a small baby. Mine, with a gauge of 4 stitches per inch, would probably fit a large toddler.
That's the reason patterns also include gauge. If the pattern had said to aim for a gauge of, say, 5 stitches per inch, we'd know that Mom should use a larger needle to make her stitches bigger, while I should go down a size or two to make my stitches smaller. In that case, we'd have matching socks at the same gauge. That's the reason gauge swatches are important, at least if you want your finished object to fit.
If you've ever wondered why a needle on one of my designs is a different size - probably a smaller one - than you'd use, that's the reason. I tell you the size that was actually used to knit the item in the photos, then the gauge you should strive for. Use a bigger needle if you have to to get the recommended gauge. Every knitter is an individual, and that's okay ... that's why there is such a thing as different needle sizes!
* Pattern: 2-needle baby socks from Marianna's Lazy Daisy Days