There is no difference, look here and you'll notice they use both 'external' and 'portable' in all three models.

You might want to make sure there is a USB cable with your purchase. There was a time it was a separate cable but now some/many/all(?) have the cord attached which saves money.

Portable generally means it is a small size external hard drive, other than size all are external hard drives.

Portable vs external - there's no standardization of terms. Though, "portable" drives are often the smaller 2.5 inch laptop drive variety, while "external" often use the larger 3.5 inch drives and so the case they're in is larger. Function and use are the same, with one exception:

The larger drives often need an external (AC) power supply, which makes them less convenient to use. The smaller ones are usually powered by the USB connection itself.

Don't be sucked in by marketing hype, drives are commodity products and most drives of known manufacturers (like Hitachi, WD, Seagate) are of equal high quality. These things are often on sale, if you look around, you're likely to find what you want in the $60-$80 range.

Also, keep in mind that all hard drives ultimately die. Think "When", not "If". If you want to be certain to have your important files (whether photos or otherwise), make two backup copies and keep one copy at a different location (like at work or at someone else's house).