Actually good point, is "SVU" the police ("Order") unit and the prosecutors ("Law") are "Sex Crimes"? Then doesn't the title after the colon undermine the premise of the part before?

I'm pretty sure "Law and Order" referring to the two halves of the episode is only a thing in the original, otherwise it's just the franchise name. SVU and Criminal Intent only had the attorneys show up occasionally, and they're the only two (US) spinoffs that lasted more than a season.

So they just worked the case and… was it at least implied that the suspects they were pursuing were convicted as the real perps?

yyyyes? Most episodes end with the arrest, if someone got arrested before X:55 then something was up (wrong guy, legal shenanigans, etc). Have you never watched episodes of SVU or CI?

No, I went to college in the early 2000s in a hilly area where we got terrible reception so I fell out of the habit of watching TV