You're mixing up a serotonin reuptake inhibitor (which binds to the serotonin transporter, causing serotonin to accumulate in the synapse) and a serotonin agonist (which directly activates the receptor).
LSD is one such serotonin agonist, i.e. binds to and activates serotonin receptors, and it is much better at this than serotonin itself to boot. Hence why people can get high off of a few micrograms of this substance. It is also selective for certain subtypes of serotonin receptors. See, your body has a comparatively small numbers of neurotransmitters, but it has to control a vast range of processes. This is done by having multiple subtypes of serotonin receptor, that, when activated, pass on different signals. Since specific parts of your brain/body will preferentially produce specific subtypes, this allows you to use the same type of signalling molecule to do different things in different body parts.
So when enough serotonin receptors of the "5HT2a"-subtype are activated, you start tripping balls. Activating 5HT3 gives you a violent urge to throw up. Activating 5HT2c causes anxiety and a loss of appetite, and so on and so forth. While all serotonin receptors naturally can be activated by serotonin, certain exogenous chemicals can bind to and activate one or more subtypes selectively, with little to no effects on others. Psychedelics, for example, are good at activating 5HT2a; and LSD is *especially* good at it, because the molecule can actually get stuck inside the receptor, keeping it activated until the body recognizes it as defective and recycles it.
As for MDMA, its primary effect is to get neurons to release serotonin into the synapses, resulting in the empathogenic effect. However, MDMA (and even more so its metabolite, MDA) also act as agonists at the 5HT2a receptor, eliciting additional psychedelic effects.
Our nervous systems, however, have evolved to be self-regulating. If receptors are continously activated, they are downregulated, which is why psychedelic tolerance builds almost instantly. However, this generally doesn't result in a crash, because psychedelics are mostly only affecting a specific type of serotonin receptor. With a serotonin releasing agent like MDMA, on the other hand, you're not just generally downregulating all your serotonin receptors, but you're actually releasing so much serotonin that much of it has to be destroyed instead of retrieved for later re-use. This means that until your stores of serotonin have been replenished, you're going to be seriously serotonin-deprived, and consequently feeling like shit.