The Collaborative International Dictionary of English v.0.48:

Monkfish \Monk"fish\, n. (Zool.)
   (a) The angel fish (Squatina).
   (b) The angler (Lophius), esp. the goosefishes Lophius
       Americanus in America and Lophius piscatorius in
       Europe, used for food. --[MW10]
       [1913 Webster +PJC]

The Collaborative International Dictionary of English v.0.48:

Angler \An"gler\, n.
   1. One who angles.
      [1913 Webster]

   2. (Zool.) A fish (Lophius piscatorius), of Europe and
      America, having a large, broad, and depressed head, with
      the mouth very large. Peculiar appendages on the head are
      said to be used to entice fishes within reach. Called also
      fishing frog, frogfish, toadfish, goosefish,
      allmouth, monkfish, etc.
      [1913 Webster]

WordNet (r) 3.0 (2006):

monkfish
    n 1: flesh of a large-headed anglerfish of the Atlantic waters
         of North America
    2: fishes having large mouths with a wormlike filament attached
       for luring prey [syn: goosefish, angler, anglerfish,
       angler fish, monkfish, lotte, allmouth, Lophius
       Americanus]
    3: sharks with broad flat bodies and winglike pectoral fins but
       that swim the way sharks do [syn: angel shark, angelfish,
       Squatina squatina, monkfish]