Your private key is composed of your view key and your spend key, I suppose the public address would work as checksum, they can all be obtained from the seed words as well. Different doors to the same room.
mymonero.com Login Options
Can somebody please explain to me the difference between logging in to mymonero.com with your private key versus your public payment address, view key, and spend key? This also may be confusing to new users of the site. I am assuming that you want to use your private key rarely, if at all, but I don't understand the relation between public payment address, view key and spend key and why you need all of them to login to the site.
What are the advantages/disadvantages with the different methods?