MDA = methylenedioxyamphetamine
MDMA = methylenedioxymethylamphetamine
They're both part of a class of drugs considered to be 'empathogens' or 'entactogens'. Though technically they're psychedelic amphetamines, they just happen to be stronger at being monoamine releasers, in this case mostly serotonin, than being psychedelics, though as they both produce quite profound altered consciousness they are undoubtedly still somewhat psychedelic.
MDA is an older drug, and was more popular in the late 60s, 70s and early 80s I believe. It's stronger than MDMA, more traditionally psychedelic, lasts somewhat longer and is harsher on your brain (more neurotoxic). Sometimes referred to as 'sass' and was once called tenamphetamine.
MDMA got popular in the mid 80s and is the most popular drug of the 'entactogen' class, or at least the one people want. It's what people mean when they say 'Ecstasy/XTC/X', 'mandy', 'molly'. Though I guess it can be confusing as MDA or mixtures of MDMA/MDA and other stimulants some would still label 'ecstasy'. It's weaker than MDA (requires higher dose), less traditionally psychedelic, less neurotoxic, and people find it more 'lovey', or produces more empathy. But some people get different reactions obviously and generally seen to prefer one or the other, or some people like to mix the two
tl;dr they're two different drugs, with similar but distinct effects, MDMA is way more popular than MDA and a little safer but which one people prefer varies greatly
Also, real high quality MDA is much more difficult to come across, especially in Europe. Also MDMA is widely faked, much more so in the past decade. I reckon MDA is faked too but probably less likely seeing as it's more of a niche product now. If you buy any drugs it's essential to use a test kit these days