I'm sure there's something I'm not understanding here because I keep thinking - the vehicle in front of you uses turn signals sometimes, right? and those flash. what's the difference?

I think the difference is that indicator lights aren't the type of flashing strobe lights cyclists use. There's definitely a much greater brightness there, plus indicators are generally a softer yellow, non-piercing light. They definitely don't have the same effect.

Turn signals on cars are usually WAY less bright than those bike lights, and flash at a slower rate. And they aren’t flashing constantly, just briefly before a turn.

Yeah the sort of flashing lights folks on their cycles trigger my vertigo, but not as bad as cop cars. The stupid new LED headlights that are absolutely blinding even on their lowest setting are a different issue. I wish people would test these things from the perspective of other drivers