Finance:It is the branch of economics that studies the management of money and other assets.In simpler terms it can be defined as the commercial activity of providing funds and capital.It addresses questions like -- what funds are required by the org & How they can be raised & 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 provides quantitative information about finances. It addresses issues like what amount of funds have been allocated to various activities, how the book-keeping is being done etc.
Both functions are distinct but complimentary to each other.
Finance and accounts are highly specilized and distinct areas and hence most organizations have seperate sections of finance and accounts.