According to my search;
1. A drama is a type of narrative writing that is meant to be performed in front of an audience. Dramas are most notably performed as plays in a theatre though many dramas have been recreated and adapted for film, TV, or radio.
2. Prose is made up of sentences and paragraphs without any metrical (or rhyming) structure. Drama is a piece of writing that tells a story; it is performed on a stage and uses dialogue.
Prose is usually written in sentences that form paragraphs. In Drama, the words are conveyed in dialogues between characters. While in Poetry, the words are penned down in lines, verses and stanzas.