[Mark C]

Sherry is wine that has intentionally been oxidized. It has some of the same flavors you'd get from leaving a regular bottle of wine sit open on the counter for a few weeks. You can buy both dry sherry and sweet sherry (cream sherry) and a few variations in between. It's traditionally made in a small region in Spain. Makes for a great cooking wine, I find it pretty similar to Marsala and have substituted one for the other in a pinch.

Port is entirely different. Made in Portugal, there are again tons of varieties, even including white ports I believe. Vintage ports are supposed to be the best, though not every year produces a crop good enough for a vintage designation. Vintage ports are the ones that typically age for 10+ years, everything that doesn't specifically say 'vintage porto' is not vintage and does not typically age long.

The biggest difference is that sherry is white, port is red (usually), and the oxidation step in making sherry imparts very unique flavors. They're both acquired tastes, though I've come across a lot more people who like port than sherry.