Heirloom Seeds 

These have been around for a long time and are unchanged. If you save the seeds, they will produce the same next year.

Heirloom seeds are always open-pollinated, but not all open-pollinated seeds are heirloom.

The seed has been saved, grown, and protected through many generations, and that history is preserved along with the seed. 

Hybrid Seeds 

These are cross pollinated, (similar to mixing blue and yellow to get green) You can save these seeds but the next year the seeds will revert back to one of their parent varieties.

Disease resistance is very often a characteristic that is sought after in hybrid seeds.

Seeds must be re-purchased each year to maintain the desired traits, although hybridization is something that with the right knowledge you could do on your own.

Non-GMO Seeds 

These are for marketing purposes only and very misleading! There are no gardening seeds that are GMO. This is a big misconception and usually cost more for no reason. 

These are more so big field crops (think like thousands of acres of field corn to feed cattle).

In my opinion, this is one category I would just stay away from all together in order to be on the safe side.

Organic Seeds

This is a personal choice/preference. You can purchase non-organic seeds for less and then use organic practices for growing them and you are on the right track. The seed itself does not matter. This is just another marketing ploy and they cost more for no reason. 

FYI "Organic" can still use sprays but have to be labeled Organic and sometimes they use the bare minimum practices in order to be certified and do not focus on quality soil.