EOS-80 (Equation of State of Seawater -1980) uses Practical Salinity measured on the PSS-78 (Practical Salinity Scale of 1978) scale that itself is based on measurements of temperature, pressure and electrical conductivity. Thus, EOS-80 did not account for different chemical compositions of seawater.  
EOS-80 consisted of separate equations for density, sound speed, freezing temperature and heat capacity but did not provide expressions for entropy or chemical potentials. Therefore, it was not a complete and consistent description of the thermodynamic properties of seawater.  Inconsistencies in EOS-80 appear for example in the heat content at high pressure, depending on which equation is used for the calculation. Furthermore, EOS-80 was not consistent with meteorological equations while TEOS-10 is valid for humid air as well as for seawater. 
EOS-80 provided expressions for potential temperature, which removes the effect of pressure on temperature but not for Conservative Temperature, which is a direct measure for potential enthalpy and therefore heat content.
In TEOS-10 the current standard for temperature scales, ITS-90 (International Temperature Scale of 1990) is used, while EOS-80 used the IPTS-68 (International Practical Temperature of 1968). In the SIA-Library of TEOS-10 implementations to convert outdated into current scales are included.
TEOS-10 was derived using absolute pressure P while EOS-80 used the pressure relative to the sea surface 𝑝. They can be converted by: P/Pa = 101325 + 10000 ∙ 𝑝/dbar (see Atmospheric Pressure).