We report a photometric study of globular clusters ( GCs ) , ultracompact dwarfs ( UCDs ) , and dwarf galaxies in the giant merging galaxy cluster Abell 2744 at z = 0.308 . Color-magnitude diagrams of the point sources derived from deep F814W ( restframe r ^ { \prime } ) and F105W ( restframe I ) images of Abell 2744 in the Hubble Space Telescope Frontier Field show a rich population of point sources whose colors are similar to those of typical GCs . These sources are as bright as -14.9 < M _ { r ^ { \prime } } \leq - 11.4 ( 26.0 < F814W ( Vega ) \leq 29.5 ) mag , being mostly UCDs and bright GCs in Abell 2744 . The luminosity function ( LF ) of these sources shows a break at M _ { r ^ { \prime } } \approx - 12.9 ( F814W \approx 28.0 ) mag , indicating a boundary between UCDs and bright GCs . The numbers of GCs and UCDs are estimated to be 385 , 000 \pm 24 , 000 , and 147 \pm 26 , respectively . The clustercentric radial number density profiles of the UCDs and bright GCs show similar slopes , but these profiles are much steeper than that of the dwarf galaxies and the mass density profile based on gravitational lensing analysis . We derive an LF of the red sequence galaxies for -22.9 < M _ { r ^ { \prime } } \leq - 13.9 mag . The faint end of this LF is fit well by a flat power law with \alpha = -1.14 \pm 0.08 , showing no faint upturn . These results support the galaxy-origin scenario for bright UCDs : they are the nuclei of dwarf galaxies that were stripped when they pass close to the center of massive galaxies or a galaxy cluster , while some of the faint UCDs are the bright end of the GCs .