How are drugs categorized as antidepressants or benzodiazepines different?

Very different: Benzodiazepines bzd develop tolerance and can be addictive. Antidepressants ad are not. All bzd effect GABA and are different only in half life and onset of action are used for anxiety or insomnia short term. Ad can help anxiety or insomnia as well as depression on a longer term basis by several different mechnisms effecting serotonin, norepinephrine, and/or Dopamine in various ways.