An apparatus comprises a processing device configured to detect an input-output (IO) pressure condition relating to at least one logical storage volume of a storage system, to receive IO operations directed to the at least one logical storage volume, to extract processing entity identifiers from respective ones of the received IO operations, and to perform IO throttling for the at least one logical storage volume based at least in part on the extracted processing entity identifiers. For example, a first group of one or more of the IO operations each having a first processing entity identifier may be subject to the IO throttling, while a second group of one or more of the IO operations each having a second processing entity identifier different than the first processing entity identifier is not subject to the IO throttling. Other differences in IO throttling can be implemented using the extracted processing entity identifiers.