I think the application developer document could use some clarification on pages 2-3 as to what constitutes "Login with XSEDE" vs. "Login to XSEDE". After talking with JP, I realized that I was not correct in equating "Login to XSEDE" to a web login to XSEDE systems like comet, stampede etc. Using XUP as an example of "Login to XSEDE" was a red herring to me since I think of being able to access compute resources directly through the XUP.
Perhaps a better definition would be to say that "Login with XSEDE" means the user can authenticate to this application with XSEDE, but it is not a Single Sign-On so the user is not also logged into other XSEDE applications like the XUP, JIRA, Confluence etc. Conversely, "Login to XSEDE" means that by logging into this application the user is also logged into all XSEDE SSO applications like the XUP, JIRA, Confluence, etc.
I think the button in the Confluence screenshot in the application developer document should then be changed to "Login to XSEDE" as it uses SSO, and the XUP screenshot should be changed to "Login with XSEDE" as JP said they intended for non-SSO to be the default.
If the difference in button wording is due to one being a SSO and the other not being a SSO, I personally think SSO should be included in the text. For example, "XSEDE SSO Login" vs. "XSEDE Login". Keeping the current wording is fine though, as long as the developer document is more clear.