This is not entirely accurate. Sell side trading usually serves two main functions:
Primary Brokerage - buy/sell on behalf of clients; arrange execution of IPO and market making
Prop trading - buy/sell on firm's capitial while traders make investment decisions
Buy side is a bit more complex. Buy side trader's main responsility is execution quality (e.g. beat the VWAP or hide the true timing and intention of the trades from the market) while the investment decision (what to buy/sell, asset allocation, etc) is made by portfolio managers. Buy side traders might use sell side brokerage service to execute some of its trades or use execution venue such as Instinet to remain anonymous. After all, some of the buy side trade might move the market or alert Prop traders on the other side if your intention become known.
Two other important concept to become familiar with are:
Chinese wall between buy and sell side
Private banking - the high end of Buy side business
