The unit of account is the unit in which prices are quoted and accounts are kept. In Britain prices are quoted in pounds sterling, in France, in French francs. It is usually convenient to use the units in which the medium of exchange is measured as the unit of account as well. However there are exceptions. During the rapid German inflation of 1922-23 when prices in marks were changing very quickly. German shopkeepers found it more convenient to use dollars as the unit of account. Prices were quoted in dollars even though payment was made in marks, the German medium of exchange.
Money is a store of value because it can be used to make purchases in the future.
To be accepted in exchange, money has to be a store of value. Nobody would accept money as payment for goods supplied today if the money was going to be worthless when they tried to buy goods with it tomorrow. But money is neither the only nor necessarily the best store of value. Houses, stamp collections, and interest-bearing bank accounts all serve as stores of value. Since money pays no interests and its real purchasing power is eroded by inflation, there are almost certainly better ways to store value.
Finally, money serves as a standard of deferred payment or a unit of account over time. When you borrow, the amount to be repaid next year is measured in pounds sterling. Although convenient, this is not an essential function of money. UK citizens can get bank loans specifying in dollars the amount that must be repaid next year. Thus the key feature of money is its use as a medium of exchange. For this, it must act as a store of value as well. And it is usually, though not invariably, convenient to make money the unit of account and standard of deferred payments as well.