DST is the universal commercial format — every commercial machine reads it and it's the default deliverable for professional embroidery shops. PES is Brother/Babylock's native format, used by most home machines. Both formats represent the same underlying idea (stitches, jumps, trims) but they store different metadata.
The practical difference is color. DST has no color information — colors live on a chart. PES stores color, so a home machine can prompt for the next thread automatically.
If you're a home embroiderer with a Brother, Baby Lock or many multi-needle home units: use PES. If you're running a commercial Tajima, Barudan, SWF, ZSK or similar: use DST. If you're not sure, use both — StichDesign includes both with every order at no charge.