What is the difference between the units 'torr' and 'mm of Hg'? According to present definition torr and mm of Hg differ though slightly.
I am still confused over it. Can someone write an explicit answer differentiating between them and the reason for differentiation as earlier they were considered same. The explanation is probably related to the changes is pressure at different heights so I want the exact definitions of these units that was used earlier and what modifications have been made?
The two units torr, and mm of Hg were the same until they were redefined.

The torr was named after the Italian Evangelista Torricelli. 1 atmosphere is $101325\ \mathrm{Pa}$. The torr is defined as $1/760$ of an atmosphere. This is equal to $133.322\overline{368421052631578947}~\mathrm{Pa}$, which periodically infinitely repeats.

The mm of Hg was defined as the pressure generated by a column of mercury one millimeter high. Since the pressure of mercury depends on temperature and gravity, it is now redefined as

$$\mathrm{0.001\ mL \cdot 13595.1~mg \cdot 9.80665\ m/s^2 = 133.322387415 ~Pa}$$ 

This has caused a difference between the units of $0.000015~\%$, so unless you require extremely high precision, you can assume that $1\ \mathrm{torr} = 1\ \mathrm{mmHg}$