Yup.
Nope, fully active pickups, at least in my experience, are relatively rare. I'd dare say that most basses with a battery just have a preamp, like the type that you'd have in a pedal or on the front end of your amp, onboard in the bass. Some basses use that preamp just for tone shaping from a neutral position, and others (like Stingrays IMO) really rely on it for their signature tone.
The Stingray pickup, despite how aggressive looking it is, is actually relatively weak given that its default presentation is with it wired in parallel. Something like a typical passive Precision with the pickup wired in series will put out a much hotter signal - I know this from personal experience, as I have both, and had a thread at one point where I expressed my surprise at the finding. Those smarter than me were quick to point out the reason, but
see here for just one other reference that I found from some quick googling.
Very cool. IMO it has the three most important elements that make a Stingray sound like a Stingray:
1. the dual-coil pickup with a wide sensing field wired in parallel
2. the pickup position in the Stingray sweet spot
3. the preamp - which, if I'm not mistaken, I believe is the same, if not similar specs-wise to its more expensive brethren
Did you pull the trigger on an amp yet?