Very slight rotational play is normal for S&Ws, Rugers, Taurii and most others.
Colt used a "tight lockup" system as did early Charter Arms and some others.
The deal on the "loose" types is that the bullet is supposed to make the final alignment between cylinder and barrel. As the gun wears the rotational slop can increase but the gun will still shoot safely.
On a "tight lockup" gun the accuracy is better when the alignment is perfect. However, if the alignment starts to drift off with use, it will STILL form a "tight" lockup but in a mis-aligned state. This is bad. At this point the gun starts to beat itself to death with every shot.
"Tight" action guns need to be checked for alignment by the user fairly frequently (as in, every few hundred shots minimum) and if it's off, send it for tuning before damage sets in.
Endshake is another matter - "fore and aft" play lets the cylinder act as a battering ram, slowly stretching the frame. This will happen VERY quickly with aluminum (or scandium) frames or those with serious power for the gun's overall weight and toughness. As one example: 38Spl ammo in a heavy gun like a Ruger GP100 or S&W 686 won't hurt it much even if there's significant endshake, but stout 357 loads might.
All of this is covered extensively in the "revolver checkout", top of this sub-forum.