Gills are those soft, thin, flexible blade-shaped ridges on the bottom of a "normal" mushroomcap. They constitute the hymenophore of the Agaricaceae, bearing the fruiting body's sexual spores on basidia.
Lamella is (in this database, at least) a more general term for any plate-like spore-bearing organ, such as those on a daedaleoidhymenophore. I do not consider those gills, as they are too hard and usually too thick and blunt.
Another marginal case is that of Cantharellus cibarius, which has frequently forking folds of various depths as its hymenophore. Even when these folds are quite deep, most fungal authors are reluctant to call them gills, as their edges are blunt (having your " gill" come to a nice point like a knife blade seems to be an important part of the concept). In most other writings, however, lamella is considered a more "precise", "scientific" term for gills.