SSRIs and SNRIs aren’t necessarily alpha blockers (although some similar drugs like mirtazipine (Remeron) have some action there).

SSRIs get their name because they are selective serotonin reuptake inhibitors, meaning the prevent reuptake of serotonin at the neuron junction, and that increases action of serotonin in that junction. And that is what causes the anti-anxiety or anti-depressive effects. SNRIs do the same thing, but with both serotonin and norepinephrine.

Many drugs have effects at other receptors (like histamine) that may cause adverse effects like sleepiness.

Beta blockers block the action of adrenaline/epinephrine at beta-adrenergic receptors, primarily found on the heart (beta-1) or lungs (beta-2). Beta blockers are primarily used in heart failure, heart arrhythmias, hypertension, and performance anxiety.

Alpha blocker also block adrenaline, but primarily in the vascular system (alpha-1). Alpha blockers are often used for enlarged prostate, hypertension, and some uses related to anxiety or PTSD.

Certain alpha and beta blockers can get into the brain and may have effects in anxiety have other effects like fatigue or weight gain.