I've been a lot of places since buying our first diesel back in 2001, and never had any trouble at all finding diesel. There are indeed two grades, #1 and #2, the former being similar to kerosene, and only useful for really cold temperatures. Almost everywhere in the US all you'll find in warmer weather is #2. Biodiesel sometimes gets added, as others have said, in blends from a couple percent to as much as 20%, with some vehicle makers insisting that no more than 5%, 7%, or 20% be used. Some states mandate biodiesel, Minnesota and Iowa come to mind here, but there are others.
Others have mentioned the various nozzle sizes. Two are supposed to be used, a large one for filling over-the-road trucks, 18 wheelers, that take a lot of fuel, and a smaller one that is used for cars and light trucks. The official smaller one is actually the same size that used to be used for gasoline. This is supposed to prevent the inattentive gasser driver from getting a tank full of the wrong stuff. However, you will find that some stations, perhaps due to laziness, will put the smaller gas nozzle on diesel pumps as well.
Some trucks can take any of these nozzles, no problem. Some have restrictor plates that allow only the two smaller nozzles, and then there are ones like on my BMW X5, have restrictors that allow ONLY the official middle-sized nozzle. This to prevent even inattentive diesel drivers from getting the wrong stuff. It should be noted that the X5 also came with an adaptor that enables you to fill from any of these nozzles, but requires vigilance because it also kills the auto-shut-off feature on the nozzle. For what it is worth, I've dragged around one of those things since 2009, all over the country, and never had to use it.
(Oh, somebody asked where to get one of those adapters. BMW dealers will sell you a kit that contains the adapter, a couple nitrile gloves and a resealable tube to keep the adapter in after you've used it. About $6 when I bought one in 2009. VW/Audi dealers also sell a similar kit, but it was $12.)