Marlin Firmware Manual Mesh Leveling
If you look into the most recent version of Marlin you will find in file Marlin/SanityCheck.h:

elif defined(MANUAL_BED_LEVELING)
  #error "MANUAL_BED_LEVELING is now LCD_BED_LEVELING. Please update your configuration."


This implies that constant MANUAL_BED_LEVELING is obsolete. It is not found anywhere else except for the file linked above. So, no, the constants are not supposed to do exactly the same. Instead an error is shown on compiling to update your configuration to exclude the constant MANUAL_BED_LEVELING.