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Yes, you're right. It's a BodyBag. Sorry for the error.
I use both BodyBags and BodyGuards. Actually, I use the BodyGuard style more often. It's pretty bombproof with the body cap on, and also lets you mount a lens, with its own cover. Here's a photo of my 1DX and 70-200/2.8L IS II, before and after a LensCoat BodyGuard and Op/Tech Snoot Boot are applied.