Systems 32bit, 64bit (x64 - x86)?

All these system specs are very confusing to me, and I would like to know a little more about how and why each of these sytems differ.
I recently replaced my 32bit system with what appears to be a 64bit Windows Vista PC system. All this has changed the way that I run and/or install programs and their capibilities. That is, I can no longer run shared folders through Network Magic, Office Groove, and my Lexar Lightning Jump drive has limited functionability,now.
So, if someone can help me to better understand what the difference is in 32 and 64 bit systems, and what is x86 suppose to be for because I have a program file that is listed as (x86). Why would a computer like mine have a 32bit control panel and features, a 64 bit operating system, and a x86 bit program file folder? what type of downloads should I be looking for? x64 or x86?
Well, anyone one who might know a little or a lot about this type of system could you please help me to better understand it?

x86 just means Intel compatible processor. Basically, if Windows runs on it, it's x86.

32bit vs 64bit:
This is just the number of data channels in the system bus. That is, a 32bit computer has 32 paths that data can travel along simultaneously and a 64bit computer has 64 paths. A 64 bit computer can move more data at a time and gives you more resources to work with. 32bit and 64bit programs are written differently to handle the system they were designed for. 64bit programs CAN NOT run on 32 bit systems. But, if you have the correct libraries and system files built into your operating system, 32 bit programs will be able to run on 64bit systems.

Vista should have some 32 bit compatibility, but being Microsoft it probably doesn't function as it should. When you are looking for programs, the best option would be 64 bit if you can find them. There are not a lot of 64bit programs around yet at this time though (for Windows anyway).

Start from the beginning.

At the beginning of PC history, there was the IBM PC (using the 8088) and the IBM PC XT (8086). Later came the PC AT (using 80286). Later yet the 386, and 486, and so on. The Intel family became known as the x86 family, even though later CPUs are called other things, like Pentium, Core, and AMD's compatible CPUs are called Athlons, and so on.

The first IBM PC was a 16-bit CPU, which means it can process maximum of 16-bits at a time. From 386 on, it was increased to 32-bits at a time. and the latest Pentium IV's and Athlon 64's can do 64-bits at a time, and are known as 64-bit CPUs. And they are ALL part of the X86 family.

Most 64-bit CPUs are backward compatible with 32-bit applications, by simply ignoring the extra 32-bits. You need special instructions to utilize the extra capacity.

Similarly, operating systems are written to the most common CPUs, 32-bit and are sometimes called 32-bit O/S. They'll run fine on 64-bit CPUs.

If you want full 64-bit functionality, you need to run 64-bit O/S on 64-bit CPU. However, this may limit your compatibility with 32-bit programs as the O/S must be able to switch between 32-bit and 64-bit modes and segregate the memory properly.

There is Vista (normal 32-bit), and Vista 64 (64-bit).

Frankly, as of now, there is NO REASON you'd use Vista 64, unless you have a program that requires MORE THAN 4 GIGABYTES OF RAM (such as a huge server, or huge analysis programs). You'd be fine with regular Vista, and avoid all the compaitiblity problems.

32 bit vs 64 bit is the way the CPU handles data, it also looks at the way that data is stored. In your old 32bit computer, the CPU handles 32 bits as one "function", which means your RAM is broken up into 32 bit chunks. The 64 bit CPU breaks the data up into 64 bit chunks, including the RAM. A side effect of this, is anyone who installs Vista on a machine that had XP on it effectively cuts their RAM in half. Since before it was in 32 bit chunks and later it's in 64 bit chunks, you lose half of the addresses.

The x86 is a refernce to Intel. Their first chip was called the 8086 chip, and when they designed their second one, they wanted it to be compatible with the first, so they kept all the things the first could do, and added. They have been doing this ever since, the plus side is any new program would (in theory) still run on the old 8086 chip, but since the speed is so low now, you wouldn't want to try it. The x86 just means your current chip is compatible with the original. In asnwer to your question about it, you should be downloading files marked for 64 bit operating systems.