Apple ID Not Accept In Pop Up Box

I have a very odd problem. When I go to my iCloud account, or even this site and go to sign in, I get the message from Apple ID, "Do you want to sign in to idmsa.apple.com with your Apple ID "name@gmail.com." The ID is the correct one. Under that is "Continue with Password." When clicked, a popup box opens that says "Enter the password for the user "Gene Surber" to continue. When I enter my password, the box shakes and is not accepted.

When I click on "Use a different Apple ID" then it takes me to the same Apple ID that is saved, and accepts my password (which is also saved). Clearly this is not a different account.

I'm not sure what is going on here, but I wold prefer to just be able to log on to iCloud and other Apple things without this happening. Has anyone else experienced this? Is it possible I have two passwords for the same account? I don't want to change the password to "correct" the problem if I don't have to as then I will have to sign out of everything and update everything. I'd just like to know what is going on and if there is a way to fix it.

[Image Edited by Moderator to Remove Personal Information]