There are many molecules with anti-depressant properties. This is not meant to be an encyclopedic review, but in general, you could divide them into four groups.
SSRIs - Prozac®, Zoloft®, Luvox®, Celexa® and Cipralex®, etc
SNRIs - Effexor XR® and Cymbalta®
NDRIs - Wellbutrin XL®
Atypicals - Trintellix®, Fetzima®
I've used the brand names here, because most people know them as such.
Selective Serotonin Re-uptake inhibitors, SSRIs, increase serotonin neurotransmission, the having a generally soothing effect. They decrease depression, obsession and anxiety, including panic. That is their intended effect. In the management of ADHD.
When there is residual depression and anxiety after the ADHD symptoms have remitted, an SSRI can take the person from partially better to completely better.
In higher doses, SSRIs can cause side effects as their effects go past soothing to numbing, which is probably the same mechanism that causes sexual side effects, such as anorgasmia.
An even more worrisome adverse effect is SSRI-induced mania, aka Bipolar III, in which the decrease in anxiety is greater and greater until it morphs into carelessness, euphoria, then risk taking and reckless behaviour,
Serotonin and Noradrenaline Re-uptake inhibitors, SNRIs differ from SSRIs primarily because they also inhibit the re-uptake of adrenaline, thus making them more energizing (in some people). They are also good for managing chronic pain syndromes in that the increase in adrenergic neurotransmission, down the spinal cord, blocks pain signals from coming up, thus decreasing both pain and suffering.
Noradrenaline Re-uptake Inhibitors, NDRIs, because they don't in crease serotonin are not pure anti-depressants. You might think of them as a hybrid between an anti-depressant and a stimulant.
Wellbutrin XL® is an extended release noradrenaline and dopamine re-uptake inhibitor (NDRI). As such in increases the synaptic concentrations of both noradrenaline and dopamine. It is officially marketed as an antidepressant, but it would be more accurate to call it a hybrid between an antidepressant and a stimulant.
It increases motivation and energy, through noradrenaline. And, it improves increases focus, impulse control and reward through dopamine. That's why it works well as an anti-smoking drug.
It does not particularly improve sadness or anxiety like the selective serotonin re-uptake inhibitors (SSRIs) do and that's why it's not really first line when someone has severe depression.
It's not a first line ADHD drug, because the magnitude of dopamine stimulation is smaller than that of the stimulants. But it works like a charm for someone who has both mild ADHD and mild depression. It's best feature is that it improves mood generally, without the sexual dysfunction and cognitive dulling that is commonly associated with the SSRIs.