I'm going through the patch list for a Community 220.127.116.11 site and when I get to the APPSEC-212 and select 1.7.x, it downloads the SUPEE-2677_EE file.
I also notice this same behavior on one or two other patches. Is it normal that for a specified patch it downloads another patch number referenced?
Yes, that is expected for some patches that you download (as they match an EE patch number). Just apply them, and they should install fine.
You can also checkout our blog for the easy guide to install all the patches,
SECURITY DISCLAIMER: The above website contains Magento Security Patch files which are self-hosted by the user and as such unsafe. Magento Forum advise all users to only download patch files from the official Magento Downloads page.