Question Aren't technically almost all shoe leathers corrected grain? ie. pebble grain, hatch grain, smooth leather, etc. the surface has been corrected through sanding or printing a pattern.
Answer: Yes, technically most non aniline dye leathers are corrected grain; box calf it is not corrected grain.
Many have a shiny acrylic wax lacquer on top (patent) and others an opaque coating (EG country calf) both often applied to the grain surface as a dye.
Many leathers come from the tannery with blemishes, wrinkles, hair follicles, scars, blemishes and/or discoloration. Other leathers are imprinted, boarded, sanded... to give them different textures (scotch/hatch grain).
Tanneries can use excellent or bad leathers and treatments to buff and correct them differ much.
For more info check to Leather Quality thread: http://www.styleforum.net/t/354137/leather-quality-and-properties
Answer 2 (from @DWFII, a bespoke shoemaker): Unless the grain of the leather is pretty much as it came off the animal, it technically has been "corrected." And yes, even high end calf skin can be "corrected." Calfskin does not come off the animal with n acrylic glaze or wax. It does not come off the animal with a pebble, or hatch grain or imprinted texture.
Aniline dye is just a type of petro-chemical derived dye. It doesn't have anything to do with whether a leather is corrected or not. Even high end "glazed' calfskin ...with an opaque top coat...was probably dyed with aniline dye. We call a leather "aniline dyed" when it doesn't have that top coat or that heavy wax, but most leathers are dyed with aniline dyes.
This question was first posed and answered in our Official Shoe Care Thread.
Have a question and can't find an answer? Try here: http://www.styleforum.net/t/228153/the-official-shoe-care-thread-tutorials-photos-etc