From what I have observed, the difference is in how you select markets to trade. Most (daytrading) futures traders pick 1-3 markets that fit their strategy and stick with them. A lot of them gravitate towards markets with high volatility and high liquidity, like Crude Oil, Nasdaq, Dax, etc. Because the implied leverage is so high, you can still possibly make a little bit of money on "dead" days.
With stocks, it's a little different, because your leverage is lower (assuming you aren't at a prop firm that gives you 10/1 or 20/1). Stocks that are volatile one day will simply not go anywhere, in either direction the next. And seemingly boring stocks will be a daytrader's dream on big news. So, your first job is to develop screening techniques that identify the stocks that should have the largest intraday moves. There are a number of realtime scanners out there that help you with this, although no scanner is perfect. Also, sometimes a big event (earnings miss/beat) will be completely absorbed after hours. The stock will gap up/down, then flatline the rest of the day. It's more about finding the stocks that build up momentum early in the day, and jumping on them.
That doesn't mean you cant have a stable of favorites - stocks that are generally volatile and liquid (i.e. AAPL, FB, etc), but it's hard to limit yourself to just a few.
