The original posters confusion seems to be not with patching, but the patch download search page.
The OP assumes that if you search for build 623860 you will get patches that apply to that build. This is an incorrect assumption.
If you search for build 623860, you will get the patch/update that contains build 623860.
So, the 'release' ESXi 5.0 update 1 is build 623860. When installed, the console displays this number. If you search for that number on the patch download page, you will get the information about build 623860 (ESXi 5.0 update 1) and the ability to download the file that will update prior releases of ESXi 5.0 to build 623860.
Patches FOR ESXi 5.0 update 1, build 623860, are any ESXi 5.0 builds that are higher than 623860.
I hope this clears up the confusion.