Generally (operative word), wider tires result in stiffer sidewalls, since a greater portion of the tire is tread, and a smaller percentage is sidewall. Stiffer sidewalls on the ‘low profile’ tires (50, 45 and 40 series and so on) are more responsive when cornering and make handling more predictable. Generally, a tire with a ‘relatively’ short sidewill will transmit more bumpage to the passengers.
Just as soft shocks cushion the road, a tire set up that uses a taller tire can help smooth the ride.
The whole thing comes down to the balance desired. Early 85 Vettes road like pogo sticks, because the engineers wantes pure numbers to advertise: numbers in the slamon, the total g’s pulled in cornering and so on. Early vettes had very very low profile tires/tyres for their day, and later models had ‘softer’ suspensions to compensate. Obviously, ‘softer’ purely relative, since in a vette it’d still be quite firm.
Again, generally, you can upgrade tires without affecting very much --even the speedo, and this might help you understand how diff tires go on the same production vehicle.
Say you have tires like this: 205/70 - 15’’. You have a modest tire on a 15" rim. Not very low profile by any means, since 70 shows that a large % if the tire is sidewall. You could go to the tire dealer, and buy up a set of 215/65 - 15" tires. What you would wind up with is a tire that is almost as tall as stock (helps keep ride height consistent and susp travel consistent…helps keep speedo pretty dead-on)…yet you would have a wider tire (but VERY likely one that isn’t too wide for the car wheel openings/clearances. VERY likely it won’t be.
You have a stiffer tire now…one that is just about as tall as the original, has a greater % of rubber as tread and a slightly stiffer sidewall. …all on the same rims.
You can even swap out rims like this, too, and not affect things. You increase to a 16" rim, but the height of the tire doesn’t change, but more ‘meat’ is used as tread.
These are popular swaps, and factories take advantage of the math involved when producing cars with diff rim and tire sizes.