A dramatic monologue is a poem that is in the form of a speech. It tends to be “dramatic” because of its theatrical feature. Dramatic monologues are used by poets to express a point of view through the words of a solitary character.
Blank verse is a poem type that’s usually written with precise meter—usually iambic pentameter—but with unrhymed lines. Playwrights and dramatists from the 1550s developed the use of blank verse in English. That eventually started the wide use of the blank verse poem type in both epic and dramatic poetry.