All correct so far.
One interesting point: just before the 357 was released, a caliber called the "38-44" was common. It was the 38spl loaded WAY hot for "44 sized guns"...more heat on it than any modern 38+P.
Some idiots inevitably put them in guns too small, old or weak. Blowups were uncommon but did happen sometimes; fast gun wear was a more common problem.
The 357 was stretched enough that the new even-higher-power 357 couldn't fit in older/weaker 38 guns, but the length difference wasn't enough to hurt 38Spl performance in the 357 guns much. So the 357 guns were meant from the get-go to be compatible with all 38Spl/+P/38-44 ammo - no exceptions.
There is a tiny accuracy cost. A few very high end revolvers can be had with your choice of 38 or 357 cylinders (or sometimes both) so you can maximize accuracy in the caliber of your choice. Freedom Arms will do this on any 357 gun they sell, offer 38Spl match-grade secondary cylinders as an option. But it's not a safety issue, it's a max-accuracy thing.