First of all, let’s talk definitions:
DRASH is an interpretation of something in scripture.
e.g. Rabbi Akiva gave a drash that explained the crowns on the letters of the Torah scroll. OR
e.g.: “That’s an interesting drash,” the teacher said, after Abe speculated that perhaps the burning bush was a door into another dimension.
D’VAR TORAH (duh-VAHR toh-RAH) (literally, a “word of Torah”) is a short teaching linked to a passage of Torah. (Please do not refer to it as a “d’var.” That means “a word of,” which is annoying; a word of what?)
e.g. Will you give a d’var Torah to open next week’s meeting?
While we’re at it, let’s look at some related D (for Dalet) words:
DRASHAH (drah-SHAH) is the same as drash, but usually refers to something more formal, like a sermon or lesson.
e.g. On the High Holy Days, Rabbi Cohen’s drashah might be as long as 45 minutes.
A DARSHAN (dar-SHAHN) is a man who gives a drash. When a woman does it, we call her a DARSHANIT.
e.g. I asked Rivka to be the darshanit for next week’s service, but if she can’t do it, ask Robert to be the darshan.
MIDRASH (mi-DRASH or MID-drash) – See What is Midrash?
e.g. The story about Abraham’s father the idol maker is a midrash.
So the answer to the original question is “not much!”