At present the standard value is defined as follows:
The kelvin, unit of thermodynamic temperature, is the fraction $\dfrac{1}{273.16}$ of the thermodynamic temperature of the triple point of water.
It follows that the thermodynamic temperature of the triple point of water is exactly $273.16 $kelvins, $T_{\rm tpw} = 273.16\, \rm K$.
The symbol, $T_{\rm tpw}$, is used to denote the thermodynamic temperature of the triple point of water.
At its $2005$ meeting the CIPM affirmed that:
This definition refers to water having the isotopic composition defined exactly by the following amount of substance ratios: 0.000 155 76 mole of $^2\rm H$ per mole of $^1\rm H$, 0.000 379 9 mole of 17O per mole of $^{16}\rm O$, and 0.002 005 2 mole of $^{18}\rm O$ per mole of $^{16}\rm O$.
The scale of temperature which is in general use is called the International Temperature Scale of 1990 (ITS-90) and thermometers are calibrated with the use of a number of fixed points whose temperature has been defined. and agreed internationally.
The reason for having this second scale is that direct measurement of thermodynamic temperature is extremely difficult and very time consuming ie not practical for most applications.