There are two types of malt and two forms of malt.. The two types are diastatic malt and non-diastatic malt. The two forms are powder and syrup.
Diastatic Malt is made by sprouting a grain like wheat or barley, stopping the growing process after a few days. The sprouted grain is then carefully dried, the small roots rubbed off and the cleaned seeds ground (milled) into a powder. The resulting powder is then packaged for sale. The malt can also be converted to a syrup. Diastatic Malt contains a collection of enzymes that help the yeast to grow by breaking down starch into sugar. Since the yeast has more available sugar to feed on, it can grow faster and better, which enhances the rise and volume of the loaf.
Non-Diastatic Malt is a substitute for sugar and does not contain the enzymes to enhance the breakdown of starch into sugar. This malt is used as a source of sugar, so in a sense it is a substitute for the starch --> sugar converting ability of the diastatic malt. It helps the rise of the dough, but only in so far as it is a sugar. In syrup form it adds a slight tan color to the dough.
The best source I've found for Non-Diastatic Malt, the sugar malt with the nice color, is the Eden Malt sold at Whole Foods Stores in the US, but I'm sure there are others that are just as good. I have used this for a long time and have come to trust it. If you use this malt, be sure to keep the top of the jar and the cap clean. If you let the malt get on the top of the jar, you will have a devil of a time getting the cap off the next time you use it. This stuff is very sticky! Store the opened jar in the refrigerator.
Diastatic Malt is usually sold as a powder. There are many sources of diastatic malt powder, ranging from the King Arthur store (expensive) to home brewing shops (reasonable). You may find liquid (syrup) diastatic malt at your homebrew store or in the catalog. I've used the Edme brand and found it very reliable. A word of advice here. Diastatic malt syrup is a living organism and the syrup is packed in cans. The malt will expand a bit and cause the ends of the can to bulge out a bit. I'm told that this is normal and that the product is not infected with bacteria, as would be the case with a bulging can of tomatoes. If you find liquid diastatic malt and the can is bulged a bit, ask the store person to explain it to you. I repeat, this is what I have been told. I have used cans of diastatic malt that were bulged and lived to tell the tale; as in so many things, use your common sense.
You can use Non-Diastatic Malt as a sugar substitute or an additional sugar. It will add a bit of color to the dough. I think it adds a bit of flavor, but I'm not sure; my taste buds aren't that good. In any event, it does seems to add a certain "something" to a dough and the resulting bread, so I use it when it's called for.
Diastatic Malt is a different ingredient. I have taken to using diastatic malt in small amounts in a lot of my breads, especially in breads that have high percentages of whole wheat or rye flour. By small amounts I mean a teaspoon for 2 pounds / 1 kilogram of flour. This seems to add a bit of rise and loft to the loaf and counter the effect of the whole wheat to limit the rise. If you get some, try it; I think you'll like it.
Yes, Virginia, you can make your own diastatic malt. It's not difficult, but it does take time -- not your time, but the passage of time. Here's a short course in making malt. You may decide this isn't worth the effort, but I like to work things out on my own. If you decide to follow in my -- admittedly shaky -- footsteps, here's how to do it.
Checking to make sure you have viable seeds.
This process makes what I call whole wheat diastatic malt, since I use the whole wheat berry, husk and all.
That's the short course in malt. You can find a lot more on the subject on the web. Look for brewing, malting, diastatic malt or similar subjects.