AMD FreeSync 2 has essentially the same function as the Original FreeSync i.e remove screen tear and screen stutter. However, there are few additional features to it.
FreeSync 2 enables the support for HDR displays.
Furthermore, with the Original FreeSync the minimum requirement for frame was 30fps for it to function, however, with FreeSync 2 that requirement is removed.
FreeSync 2 also improves the input latency of the monitors making them better for giving a more competitive edge to the players.
Another important difference between the two is that FreeSync 2 requires AMD validation before they are produced.
As such, FreeSync 2 monitors are more expensive and usually high performing. The Original FreeSync did not require validation from AMD and was completely open. Therefore, it could be fitted on any monitor.
That is the reason why it is the most widespread adaptive sync technology in the budget monitors.