Market neutral is different from a long/short fund.
Market neutral funds typically try to achieve a rate of return that exceed the risk free rate by 300 to 600 bps. These funds are generally macro in nature and hold a variety of assets including equities, currencies, sovereign debt, etc… the fund attempts to hold a zero beta, but this is rarely achieved. think absolute return
Long/Short funds basically describe your plain vanilla equity hedge fund. The fund is long those stocks it thinks will provide alpha and it is short those stocks that is believes to be overvalued. Generally these funds will have varying degrees of exposure to the long positions and short positions in their portfolios.