What is the difference between x64 and IA-64?
x64 is used as a short term for the 64 bit extensions of the "classical" x86 architecture; almost any "normal" PC produced in the last years have a processor based on such architecture.
AMD invented the AMD64 extensions; Intel was more or less forced to implement them, and called them first IA-32e, then EM64T and finally Intel 64 (actually, the AMD and Intel extensions aren't exactly the same, but they are almost identical).
Many people also call this stuff x86-64, to have a vendor-independent name and to stress the fact that it's the 64 bit evolution of the x86 architecture. All the "regular" PCs that are sold with "64 bit processors" run on x86-64 architecture.
IA-64 (Intel Architecture 64) is an almost completely unrelated 64 bit architecture (also known as Itanium), developed by Intel initially for high-end servers. It was said that Itanium could have been a replacement for the x86 architecture, but this architecture didn't have much success (for various reasons), so it's unlikely that you'll ever need the IA-64 installers.
For more information, you may have a look at the wikipedia articles on x86-64 and Itanium.
IA-64 is the Intel Itanium Architecture. This is a Very Long Instruction Word (VLIW) processor instruction set.
x86_64 is the normal 64-bit architecture that is used by processors inside every laptop / desktop in today's computers. This processor is a dynamic processor.
The main difference between these two is that
In VLIW, the compiler resolves the dependencies between instructions and schedules them appropriately. The processor merely executes them.
With a dynamic processor, the compiler just schedules the instructions without worrying about dependencies. The processor takes care of dependencies, reorders them and executes them appropriately.
VLIW code is dependent on each chip's internal architecture. The compiler needs to know that information. The advantage of them is that it can extract much more parallelism than dynamic processors can give.
The code is independent on each chip's internal architecture for dynamic processors. It just needs to follow the instruction set. So code compiled on one machine can run on other machines very easily. The disadvantage though is that limited parallelism can be exploited from dynamic processors. And the internal logic and design is very complex and intricate than VLIW.
Nevertheless, dynamic processors are used today mostly by consumers (individuals), so they can run code compiled / generated on any machine. VLIW processors are used by servers and enterprises because of the parallelism they can produce.