A common exchange within the average hardware store:
Customer: I need a new supply line for my kitchen faucet.
Employee: Very good. Do you know what type of threads were on your old one?
Customer: I think they were just the "normal" threads.
Such are the common mistakes made by a great many DIYers who have not had any real plumbing experience. The problem here is that there are no "normal" threads in plumbing. There are very few cut-and-dried instances where only one type may be used. There are some which are more common than others, to be sure, but rarely are there certainties.
While common projects, such as replacing a supply line, are fairly simple and can generally be done by the average homeowner or renter, issues like this are commonplace. Inexperienced plumbers often forget to bring the old part in with them (which would solve this problem veyr quickly) or they forget to really look at the old part in order to see what kind of fittings were on either side.
What makes this even more difficult is that in addition to plumbing threads comming in different sizes, they also come in completely different styles, all of which serve very specific and distinct purposes. Common supply lines, for instance, generally have a 1/2-inch pipe thread on the end which attaches to the faucet, and one of three sizes on the end which attaches to the valve - 3/8-inch compression, 1/2-inch compression, or 1/2-inch FIP.
What does all this mean?
The most common plumbing thread are standard, tapered pipe threads. On the packaging for products utilizing this thread it will say either MIP (male pipe thread), FIP (female pipe thread) or NPT (national pipe thread). These are the standard threads on galvanized, black iron, pvc, copper and other pipe fittings. These threads are tapered in order to create a water-tight seal, but they must be used in conjunction with teflon thread tape or joint compound in order to function properly (white teflon if used with water, yellow if used on gas-carrying iron pipe).
Compression threads are much smaller than pipe threads, as they are measured using the size of the corresponding pipe (usually copper tubing), rather than the threads themselves. As a result, they can be very confusing for the average consumer, who can't understand how a 1/2-inch compression thread can be so much smaller than a 1/2-inch pipe thread (shouldn't they be the exact same size?).
Compression threads are not tapered, which means they should not be used with teflon tape (teflon tape or other joint compounds can actually prevent them from sealing). These threads are most commonly used to create a water-tight seal over copper or plastic tubing, in conjunction with a metal (or plastic) ferrul (the compression nut tightens down on the ferrul, which "compresses" onto the pipe, hence the name). These threads can be found, however, in other situations.
The aforementioned situation with the faucet supply line, for instance, often uses compression threads. Angle Valves often use compression fittings to attach to copper pipes coming out of the wall, then have another compression fitting for the supply line (the reasoning here is that one could potentially use copper tubing in order to make a supply line, rather than buying a "prefabricated" one, though this is becoming more rare).
Compression fittings can show up in other odd places, however, so it is best to watch out for this.
Flare fittings often show up in automotive and gas-line applications, but they can exist in standard home plumbing as well. These fittings, like compression fittings, are not tapered, so teflon tape should not be used with them. They are used in copper tubing applications, where a special "flaring tool" is used to put a flare on the end of a copper tubing, which seats down inside a flare fitting, which then threads onto another fitting, causing the copper to seat neatly down onto the fitting's "seat."
Flare fittings are often very confusing to the average DIYer because they are very close in size to standard pipe-threads, but are not at all interchangeable. In addition, where pipe threads only exist in certain, very specific sizes (1/8", 1/4", 3/8", 1/2", 3/4", etc.), flare threads exist in different sizes, such as 5/8" and 15/16".
Finding the Right ThreadWhile it can be difficult for all but the most experience plumber to be able to tell by sight which style of thread is which, many hardware stores have sizing guages or charts which can help to determine which fittings or adaptors are needed for each application. So, once again, the best course of action is to bring parts into the store. If nothing else, the store employees can simply try the different available fittings until they find the ones that work.
It is for this reason that plumbing can be a very difficult, time consuming process until one gets the hang of it. Simply understanding a bit about the different types of threads, though, can hopefully help to ease a bit of that frustration.