Finance: It is the part of economics that studies the management of money and other assets. In easier terms it can be explained as the commercial activity of providing funds and capital. It addresses questions like -- what funds are needed by the org? How they can be increased? How they have to be allocated etc
Accounts: It is the occupation of maintaining and auditing records and preparing financial reports for a business. Accounts give quantitative information about finances. It addresses issues like what amount of funds have been due to several activities how the book-keeping is being done etc