Different. If the pain is from hard skin, you have a corn or callus. Basically they are the same tissue, with a corn being more focal and a callus, more diffuse. A bunion is the boney enlargement where the big toe and the metatarsal behind it meet. The big toe is usually leaning toward the lesser toes. If the boney lump is on the toe itself, this is an exostosis. See a podiatrist for discussion of treatment.
Pain. As stated it could be both. See your podiatrist for an exam and x rays ad this will be explained to you as well as treatment options.
Could be either. . Or both. If you elect to have the bunion surgically removed, there are several ways your surgeon could go about it. Depending on the angle of your bones (you'll need an x-ray), there are many different procedures to choose from to correct your foot. Once the bunion joint is corrected, calluses and corns will often go away over time, depending on their location.
Need more info. It could be either.
Could be either/both. See an orthopaedic foot and ankle surgeon in your area. Find one at www.Aofas.Org.