Gel is a recent newcomer to the mattress space. It is being used as both a standalone layer and an infusion into foam. Gel benefits mattresses by retaining less heat than memory foam. Also, newer gels compete against memory foam by being more responsive and less toxic.
Gel is similar to foam because it is a polymer made by blending plastics and other chemicals.
Because of gel's heat diffusing properties, it is generally found in the top layer of the mattress under the cover.
Pros: Cooler sleeping surface vs memory foam. More responsive feel when not combined with foam.
Cons: Similar to foam, it is a synthetic blend of chemicals.
A hybrid mattress blends foam and pocket springs in one mattress. Usually this involves a more substantial foam layer than other mattresses that are marketed as innerspring.
A hybrid mattress offers a 'best of both worlds' type feel, where there is added support from the pocket coils and a comfortable, pressure point relieving surface.
Though there are latex and memory foam hybrids, the feel of them can be quite different because of the response of the latex vs the memory foam's slow response.
Pros: Best of both worlds with memory foam / latex and pocket coils provide ultimate comfort and support.
Cons: Beware of the foams being used as some hybrids still off-gas or sag because of lower quality materials.