Are corn kernels considered a grain
The grain of corn is known as a caryopsis, which Merriam-Webster defines as:


  a small one-seeded dry indehiscent fruit (as of corn or wheat) in
  which the fruit and seed fuse in a single grain




This image by Encyclopedia Britannica shows that the corn seed, enclosed by the seed coat (testa) is then further surrounded by the pericarp, which consists of the layers of tissue around the fruit. 

Therefore, the corn kernel can be described as any of the terms that you have mentioned.