When you say Generic battery, it means that it’s just a basic battery pack without the elegant packaging and some features, maybe the warranty has a short duration as opposed to the genuine B&D batteries which usually have a three year warranty. You can also get them in improved version, maybe two times as big and last twice as much. Or something that uses a different kind of battery cell like NiMH which can hold more charge than NiCad with the same amount of battery cell.
Not every replacement battery are good, some third party company who just want to gain money uses a very low quality components to lower its cost. What happens is the plastic covering and the lock mechanism easily breaks when you drop or bump it, making it useless for just a couple of days. Some even cut down the volume of battery cell and actually don’t last long than it intended to be. So, be cautious when ordering a Black And Decker 24V battery, you might end up throwing away cash instead of saving.
If you plan to order it online, since you cannot actually see the unit, what you can do is do some study about the merchandise. Read some testimonials from individuals who actually bought and used the product. If you can, try to find more opinions from different websites, often people are biased and tell only the good things about them and not the negative part.