Accounting deals more with book keeping, credits, debits, etc. In short, it deals more with itemized profits and expenses. Finance deals more with capital markets, stocks, bonds, options, futures, managing money, etc. Accounting is more about micro-money issues and finance is more about macro-money issues.
This is a great question: Accountants keep the score and Finance spin the results, basically… There is more money in Finance but more jobs in Accounting, as far as I can tell...
Finance deals with raising money for a particular project while accounting deals with counting your money when the dealing's done.