For the majority of people a fine hurts.
However, as you say a fine to some is just a number and in those cases another form of punishment would be more apt.
For instance if a person on an average income got fined £100 for letting his dog sh*t on a footpath, that would probably act as a deterrent and next time his dog does it he clears it up.
To a millionaire a £100 fine would be just, as you say, a number and it wouldn’t bother him if he got fined that amount regularly. If he wasn’t fined and instead made to pick up the entire dog sh*t in the area every day for a week, then he would think again.
The only problem is proving his wealth to determine that £100 fine is meaningless to him.