Monteggia Fracture
Monteggia fracture occurs from a blow to the proximal ulna (eg, impact from a police batton -- like nightstick fracture). Here, in addition to proximal ulna fracture there is also a dislocation of the proximal radioulnar joint.
Galeazzi Fracture
Galeazzi fracture is the mirror opposite injury (emphasize this point with bidirectional arrows). It occurs due to blow to the distal radius. There is fracture of the distal radius and dislocation of the distal radioulnar joint.
We can remember these mirror opposites with the acronym "MU-GR" for Monteggia Ulna - Galeazzi Radius". The MU comes first to remind us that this is a proximal ulnar injury whereas the GR is a distal radial injury.