Two different plants. 'Nigra' is a cultivar of Thuja occidentalis, or northern white cedar. 'Green Giant' is an interspecific hybrid of Thuja plicata, or western red cedar, and Thuja standishii, aka Japanese arborviatae. All such plants are commonly called arborviataes, an old Latin epithet meaning tree of life. Drinking tea made from the foliage of such plants saved early explorers from the disease scurvy, being high in vitamin C. Oh, should mention, none of these are true "cedars", that being yet another conifer grouping.
Read up on the characteristics-much info available online. And while what follows is opinion, it is the opinion of a lifetime lover of all things Thuja: I really hate 'nigra'. Multistemmed, the foliage doesn't hang right on the plant, there's just nothing I like about it. But please, I'm obsessive about this stuff! I would like GG if it was winter-hardy in the area whee I do my work, but it has proven not to be. I also much, much prefer the look of wild plants. Just straight species T. occidentalis is already a dense and rather slow-growing plant. What they've done with their selections, ie landscape cultivars, is taken that characteristic to an extreme. There are places for such, but like I said, I'm into something else.
Finally, where are you? That will have at least some bearing on what you end up using.
+oM
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japanese maple
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