You should seek to understand this in two parts: 1) what each of these are technically and 2) what each of these do. So with regard to (1), you can run either reducing or non-reducing SDS PAGE. SDS is a denaturant and it coats the protein with charge so that intrinsic charge no longer matters and the proteins migrate according to size. But SDS does not break disulfide bonds under non-reducing conditions and if your protein has this, it could mess up your gel because then 3D shape will matter and the proteins won't just be moving by size. That's why the majority of gels are run under reducing conditions (reducing SDS), which disrupt the disulfide bonds and makes the proteins truly migrate due to size. These two methods offer a good way of telling whether your protein 1) has disulfides (different gel pattern) and 2) whether those disulfides link up subunits/domains (getting 1 band in non-reducing and then 2 bands of comparable smaller size in reducing SDS).
Finally, native PAGE is run in the absence of SDS and since SDS is a denaturant, the protein runs in its native, or folded, form. This is not very useful for quantitative purposes but is very useful if you're trying to figure out if your protein is globular or has a lot of beta strands. Sheets will present a larger surface area and thus draw more drag whereas globular proteins will migrate quickly. Experimentally, you would run one of these with several other known globular and beta stranded proteins so that you can compare.