No, "3D camera" is not the same as "stereo camera".
A stereo camera takes two images at the same time (either via two separate lens / sensor sets, or via a mirror system to split the frame of a single set into two views). The two images produced by these cameras are regular images; they don't make one for the image and one for the depth map.
Such a camera (image + depth) is possible, but it is another type of 3D camera, not a "stereo" camera (they are sometimes called "depth camera", but this label can also be applied to a camera that does not produce depth maps without producing an image).
Some other 3D cameras use more than two lenses. You will find that these almost always use film rather than a digital sensor. These are sometimes confusedly called stereoscopic multi-view cameras (stereo meaning two and multi here means more than two), but also sometimes called lenticular cameras, since the production of lenticular prints is their main use. (Lenticular prints using more than two images have a better 3D effect because you can tilt the print to "look around" in the scene.) Eg. the Nishika 8000
With a depth camera, you can produce synthetic images of views close to the raw image, which allows you to create stereo images or multi-view images (also suitable for lenticular prints, or simply to move them 3D images .gif). This process struggles with the translucency and reflections of the image. Since these entities are the result of sources at more than one depth at a given pixel location, they cannot be correctly captured by a single image and a single depth map.
Stereo cameras (dual view) handle transparency and reflection very well, but you will only have to be content with stereo images (or apply post processing to synthesize a depth map)