Hello, I need an external hard drive (to store photos, and when I get a new laptop, to back up my other files). I purchased a Seagate 500mb portable hard drive yesterday (still in packaging) but I saw a desktop Seagate drive today, cheaper... I don't really need a portable drive (at the moment)but is there any other advantage to keeping the portable? The desktop runs at a higher speed, although it uses a power adaptor (yet another cable)... I've never had an external drive before, so any advice appreciated. Thanks.
Save for being able to bring the data around with you, there really isn't an advantage to an external drive (at least in my opinion). Yes, an internal will require a power source, but chances are that your desktop has plenty of sources for another HDD (unless you have an older desktop, which in that case you'll need to get an adapter).
The terminology is confusing, but I think you mean this:
You have bought a new "portable" hard drive that is kind of small and has only one cable that connects from the unit to a computer port - VERY likely as USB2 port. It has no extra power supply block, and gets all its power from the USB2 port. It MAY actually have two connectors on the end of its cable to plug into two USB ports to get enough power.
Then you saw a different kind of external HDD unit labeled a "desktop" external drive. You are NOT actually talking about a INTERNAL bare drive intended to be mounted inside a desktop machine. This unit is larger and has both a cable to the computer and a separate power supply module. Its interface to the computer may include USB2, but probably also includes another type of interface like eSATA or Firewire. You only use one interface type at a time.
There are three issues here.
1. Units sold as "portable" vs. "desktop" external hard drives. The "portable" ones typically are smaller and lighter and contain physically smaller HDD units inside like those used inside laptops. They use less power and often can get enough power to run from the USB port (which has a limit on how much power it can provide). However, these disk units are more expensive per GB of capacity, and are not made in VERY large capacities anyway. The "desktop" ones typically are larger and contain the same type of common 3½" HDD units inside that are used in desktop computers. Because they are common, their cost per GB capacity is much less, and because they are physically larger they can be made to larger max capacity.
2. There are three common interfaces between an external drive and the computer: USB2, eSATA, and IEEE 1394a (aka Firewire 400). Many external units come with two of these, some with all three. Among them, USB2 is the slowest, but is so VERY common that you can be guaranteed any computer you approach will have a port to connect to. eSATA is faster (almost as fast as an internal SATA connection), but you MUST have an eSATA port on the computer. (Well, many such external drives come with an adapter plate so you can create an eSATA connection point from a plain internal SATA port.) Likewise, IEEE 1394a (aka Firewire 400) is almost as fast as eSATA but requires a port of this type on the computer. More recently USB3 ports are coming out on computers, and they are backwards compatible with USB2 so you can mix and match. BUT USB3 is much faster - pretty much matches eSATA speed - so if you can get this in an external disk unit, do so. You can use it on any old USB2 port at the older speed, and on any newer machine with a USB3 port at faster speed. The much less common option is IEEE 1394b (aka Firewire 800) which is the fastest of all these, but not a common port on a PC machine.
USB ports have limited power available to connected devices, which is how "portable" hard drives can work without an extra supply. eSATA in its original form does NOT have power available in the port, but there is a newer version that has limited power. Firewire ports come in two varieties that look different at the connector. The larger 6-pin version has limited power available, the smaller 4-pin version does not.
When you said the "desktop" unit was "faster", I suspect strongly that the difference is in the interface. I have no doubt the one you bought first is USB2 with limited power in the port, but the slowest of these three interfaces. The second unit you saw may have a higher speed spec, but ONLY on an eSATA or Firewire port. IF you use it via USB2, it will be the same slower speed as the other unit. (Well, there may be another small difference: the "portable" unit may actually be using inside a slower HDD to reduce power consumption.)
3. External units of the "desktop" variety containing the larger HDD's inside use more power that "portable" smaller units - more than you can get from a USB connection, usually - so they come with (they require) their own extra power supply. They cannot run without it because they draw no power from a USB port. Personally, I prefer the "desktop" types with better price and capacity, and no power drain from the computer's USB port. I don't carry mine around in a pocket.