Here’s an article from Analog Devices detailing the differences between current-sense amplifiers and difference amplifiers in high side current measurement. Current sense amplifiers offer measurement of the instantaneous current, while difference amplifiers offer average current measurements. While current-sense amplifiers offer better current consumptions and lower noise, the difference amplifiers are more robust.
Both types of current monitors can do the job, yet the advantages offered by their different architectures are accompanied by distinct trade-offs. For instantaneous current monitoring, the wide bandwidth of current-sense amplifiers is most suitable, while applications monitoring average current can be easily served by a difference-amplifier topology.