Action is about conflict. Whether with guns, blades, fists, or mysterious powers, these anime feature characters in combat - either to protect themselves or the things or people they value, or simply as a way of life.
Drama anime heavily emphasize their characters' emotional development. Whether by experiencing the protagonist’s emotional turmoil, viewing heated character interactions, or exploring a passionate romance, any anime that humanizes its characters through emphasizing their flaws qualifies as a Drama.
Mystery anime focus on unresolved questions, and the efforts of characters to discover the answers to them. Whether curious and deadly events are afoot, or some part of the world itself is strange or inexplicable, or someone's past or identity seems strangely shrouded, these characters are set on learning the truth.