I think there's a couple of thing said there that can be confusing. First there's the issue of Debian and Ubuntu. As I understand it, Ubuntu is a distro that is built upon the foundation of another distro called Debian. So in that sense, Ubuntu IS Debian in that it uses a lot of code from Debian, adding their own code on top of that.
The other thing I saw in that thread that might lead to confusion is the mention of packages for 64bit architecture. when you use precompiled packages for your system, you need for those packages to be compiled for your architecture (32bit or 64bit). This is irrelevant of Ubuntu or Debian, it is the compiled packages of those software packages destined for either 32bit processor or 64bit depending on your needs.