The OpenGL wiki says that in order to use stencil buffer attachment with depth buffer in FBO one needs to create the render buffer with format of the type GL_DEPTH24_STENCIL8, as it seems like GL_STENCIL_INDEXX aren't implemented.
What I don't understand is whether such a buffer is also depth buffer if I set it as GL_DEPTH_STENCIL_ATTACHMENT? Or should I still create separate depth render buffer with formats (GL_DEPTH_COMPONENTXX)?
It's not that the STENCIL_INDEX formats aren't "implemented". It's that the specification does not require an implementation to consider them to be complete. Implementations are allowed to reject a combination of image formats for whatever reasons it deems fit, unless you stick to the list of required image formats.
A depth/stencil image has depth and stencil in it, just like a red/green image has both red and green in it. So yes, you attach the same image to the GL_DEPTH_ATTACHMENT and GL_STENCIL_ATTACMENT points. Or you use GL_DEPTH_STENCIL_ATTACHMENT as shorthand for both.
