A Eurocurrency deposit is a deposit with a bank in the currency of a country which is not the country in which the bank is located, e.g. the deposit of sterling pounds with a bank in USA or a deposit of US dollars with a bank in UK. Most bank deposits of currency outside the country of the currency's origin are in US dollars and so the term "eurodollars" is occasionally used to describe all eurocurrencies.
The eurocurrency market describe the depositing and lending of eurocurrencies. In other words, the eurocurrency markets are international money markets in which:
(a) Banks obtain deposits of foreign currencies and re-lend them, often to other banks; or
(b) Banks borrow eurocurrencies from other banks and then re-lend them