The Exchequer Great Seal is the seal used by The Court of the Exchequer. This Court now has a single judge known as 'The Queens Remembrancer' who holds the seal. Although the Court now consists of a single judge, the seal is still used on some important state documents.
The function of the Court, when first convened in the 12th. century, was to examine and 'try' the accounts of the King's Revenues. The judges were known as 'Barons of the Exchequer' until the court was merged in the 'High Court of Justice' in 1875. The only trials now carried out by the Court are the annual 'Trial of the Pyx' where the standard of the metal used for the coinage is judged and a verdict given by a jury of goldsmiths.
Little information is currently available, but it would seem that the 'Great Seal of the Exchequer' is always smaller than the 'Great Seal', has a reduced version of the 'Great Seal' obverse/seal (three quarters of the size), and an armorial reverse/counterseal. The counterseal also carries the legend 'SIGILLUM SCACCARII'.
Shown below are images of the 'Exchequer Great Seal' of Queen Elizabeth II.