The small portable drives are the ones that connect using only a USB cable, and utilize a 2.5" hard drive. The portable hard drives are small because people prefer to have a smaller means of storage that can also connect easily. The 2.5" portable drives also have a much larger capacity than any flash drive you could buy.
As you realized, the 2.5" hard drives are the ones which go into a laptop because of space requirements. Also, the 2.5" hard drives are almost exactly like a larger 3.5" hard drive, except that they are smaller due to miniaturization of all the parts used.
As PohTayToez said, the parts are miniaturized. This is made possible in large part because of much tighter tolerances between parts. Though it's also due to the modern ability to make parts MUCH smaller than we've ever been able to do. However, this also means that the smaller 2.5" hard drives are more susceptible to damage from being roughed around, or drops, etc.....
The larger desktop external hard drives are a 3.5". This is the size most commonly found in desktop computers and also desktop external hard drive enclosures. They can hold about the same amount or a little more than the 2.5" hard drive.
The benefit to the larger 3.5" hard drive is that the manufacturers do not have to try and shrink everything down so small. This makes the 3.5" drives easier to produce and that means lower cost of manufacturing, and a lower cost for you! Also some 3.5" drives also even incorporate design extras such as a heatsink into their casing to help dissipate any heat generated during use. Manufacturers can incorporate things like heatsinks because the 3.5" drives are larger and are usually installed/used in places where there is the room for the "extras".
The 3.5" drives typically require both a data connection as well as a power connection as they require more power than a smaller 2.5" does. The desktop external 3.5" drives are more commonly used for major backups. They are also used for long term storage, or anything really large you need stored but don't want taking up space on your C: drive.
For instance I have both a 2.5" external and a 3.5" external drive. My 3.5" is for my backups, and other large folders/files I don't want taking up large amounts of space on my C: drive. I use the 2.5 for storage/transfer of files/folders for easy access when I'm on the road.