Think of it this way: The Artistic Director of the theater
usually is in charge of all the creative decisions --
which plays to produce for the season, which
directors to hire to helm the plays, etc, etc.

The Managing Director is in charge of the theater's
business affairs such as you indicated above --
marketing, grants, finances, etc.

Sometimes they work hand-in-hand. Other times
they butt heads.

For example: The Artistic Director may decide next
season they are to do a new play, an avant-garde
piece, or a Shakespeare production.

The Managing Director will tell them that ticket sales
and market research indicate their audiences don't
want to see new or weird pieces, but familiar
chestnuts and musicals.

Sometimes they compromise with the Managing
Director allowing an avant-garde show if the season
also includes a remounting of "Guys And Dolls."

The Artistic Director finds a director and designer for
the show; The Managing Director determines how
much they'll be paid.

The A.D. pushes the envelope; the M.D. watches the
bottom line.

Etc, etc.

Hope this helps. Good luck to you.