EDIT: A little late on this post (other people have already answered), but on second thought I'll put this up anyway.
MDA is a substance that's very similar to MDMA, except with a slightly longer duration, a harsher body load, and a mild psychedelic edge. Some say it feels "speedier" and less empathogenic, but that's getting on the subjective side.
Other people really enjoy it, with some opting for a mix between the MDMA/MDA. MDA is both more acutely toxic and more neurotoxic than MDMA; both the acute toxicity and the neurotoxicity are likely due to it playing the more traditional amphetamine role of releasing large amounts of dopamine and norepinephrine (in addition to serotonin, of course).
There are a few other chemically related substances in the MDxx family, but of less note. MDEA/MDE is another common MDxx compound, with a slightly shorter duration and more of a "stoned" or "floored" feeling to it. MDMC is the last in the family proper, but it unfortunately only has threshold effects and is of little recreational interest.
EDIT 2: On the methamphetamine issue: MDMA is actually closer to methamphetamine than MDA is; note that MDMA = 3,4-methylenedioxy
methamphetamine whereas MDA is simply 3,4-methylendioxy
amphetamine. The reason for this difference in naming is simply the presence of a methyl group, which in general makes the molecule more stable and lipid-permeating.
The big difference between the infamous methamphetamine and MDMA is not the name, but their releasing profiles: methamphetamine is a potent releaser of dopamine, norepinephrine, and serotonin, whereas MDMA/MDA/MDEA primarily release serotonin (with a fair amount of dopamine and norepinephrine on the side, which are responsible for their euphoric and stimulatory effects). Since methamphetamine releases so much dopamine, especially in the mesolimbic pathway, it's strongly physically addictive. Methamphetamine reacts decently to redosing, so users can take meth repeatedly. Methamphetamine can also be smoked, increasing its addictive potential. Meth is usually sold in forms that are capable of being injected (e.g. crystal or powder), further increasing its addictive potential. MDMA, on the other hand, cannot be smoked (it'll burn before it vaporizes in its normal form), and is usually sold in pill form, which discourages injection. Most people -- rightly -- won't trust MDMA for injection even when it's in powder form.
In my opinion, it's mostly the massive dopamine release and the faster routes of administration that differentiate methamphetamine from the MDxx's, not a qualitative difference in the way that they work.
