Len, let me clear this?
Are x86_64 and AMD64 the exact same thing? Can they run ordinary x86
apps?
Yes, both refer to AMD64. The can both run 32-bit apps.
In fact if running a 32 bit kernel it should behave identically to a
normal 32 bit x86 processor.
If running a 64 bit kernel, 32bit programs can be run. However by
default the debian AMD64 port does not support this because it would
require 32bit libraries which are a major pain. But most users of
Debian AMD64 would have no reason to run 32 bit programs unless they
wanted to run certain non-free programs, or one of the few programs
that currently don't compile/run right on AMD64 such as WINE and
OpenOffice.