But in many cases the differences are significant, and important. It may help you to pre-scan and create lists of stocks with different characteristics, prior to back testing and forward testing. For example, EPS (earnings), dividends, TR(Range/Volatility), industry, etc. etc.
As just one example, at one time I traded a "pullback" system that looked for weakness in equities. I scanned and created a list of stocks that had strong volume, and strong and growing EPS (profits). The reasoning, which worked, was that buying into technical weakness on otherwise strong companies was preferable to just buying into a random list.
This takes time, but you may find that there are one or two specific characteristics that respond well to your strategy, or to a new strategy.