I agree that some terminology could make it easier. I think "key" is an ok choice for the private key, but for the public key I think there could be a better analogy. Calling them the same thing is a bit confusing and people don't understand that one of them you give away, while the other is confidential.

When I explain it to people I tell them that their public key is like an unlocked lockbox that you give people into which they can put a private message. They can close the box to lock it, but once they shut the box only you have the key to open it.

It's not a great analogy but it seems to me that the public key does not make sense as a "key" to the average person.