Architectures usually refer to the difference between 32-bit x86 (i386) and 64-bit x86-64 (amd64/em64t) processors. Both are distinct architectures. Use a tag specific to one architecture when a problem is believed to be architecture-specific.
For example, if you're having a problem just with the amd64 live CD, and the i386 live CD worked fine, tag your question 64-bit. Note that some architecture-specific problems are bugs (and Ask Ubuntu is not the place to report bugs, as detailed here).
Ubuntu supports the following architectures:
- amd64 (x64)
- i386 (x86)
- PPC/PowerPC (Old macs) -- This is unofficial.
A processor that can run the amd64 architecture can run the i386 architecture also, as the processor is backward-compatible to a 16-bit architecture. Generally, most OSes start in 16-bit mode, then, very early, switch the CPU to i386, and optionally, amd64 mode.
For questions about running 32-bit Ubuntu software on 64-bit Ubuntu systems, use the multarch tag.
The architecture tag should not be used in the sense of design principles and decisions (unless, of course, they are also about computer architecture as described above). For such questions, please use the design tag instead.