Supersonic
Supersonic speed is a rate of travel of a bullet that exceeds Mach 1 - the speed of sound. For bullets travelling in dry air of a temperature of 20 degrees celcius at sea level, this speed is approximately 343m/s (1125f/s). When shooting, the atmospheric conditions will very rarely match these mentioned above, therefore this speed of 343m/s being the beginning and end of supersonic bullet flight can only be used as a guide.
Transonic
In ballistic terms, transonic refers to the condition of bullet flight in which a range of velocities of airflow exist surrounding and flowing past a bullet that are simultaneously below, at, and above the speed of sound in the region of 343m/s.
When a bullet slows to transonic speed, it is approaching the sound barrier. This has a destabilizing effect on spin-stabilized projectiles, which is not good. The bullets center of pressure shifts forward during this stage, and the question must now be asked whether your bullet has enough gyroscopic stability to overcome the increasing dynamic instability experienced during this transonic phase. Some bullets do this better than others. This is different for each bullet, cartridge and rifle combination, but projectiles with a higher ballistic coefficient will overcome this transition smoother than those with lower BC's.
Once a bullet reaches its final transonic stage, it is now entering subsonic speeds, and the flight path of the bullet is altered. Predicting the trajectory becomes very difficult, if not impossible. At this point, generally the weapon has reached its maximum effective range.