When to run a blank using ICP-MS
This terminology is specific to EPA and it is not universal, because there are so many legal issues associated with any environmental analysis. They have to be extremely careful at each and every step (it may cost someone millions because of a wrong analytical result). Hence the reason for various "blanks." The language of those methods is official and the steps are highly detailed. Hence these robust methods can be defended legally using the terminologies used in the methods.

While preparing a calibration curve by ICP or any other spectrochemical technique, there can be only one blank, which sets the baseline reading. One would run this blank and 5-6 standards. So which blank is this? By EPA nomenclature, this is the calibration blank, which is defined by them as "Calibration Blank – A blank solution containing all of the reagents in the same concentration as those used in the analytical sample preparation. This blank is not subject to the preparation method." Pretty much standard definition.

So what are the other plenty of blank solutions doing? They are used for quality control after the calibration to check the accuracy of the instrument, method, operator etc. One can test them right after performing the calibration process. See how specific the directions are:

a) Laboratory Reagent Blank (LRB) – An aliquot of ASTM Type I water that is treated exactly as a sample including exposure to all labware, equipment, solvents, reagents and internal standards that are used with other samples. The LRB is used to determine if method analytes or other interferences are present in the laboratory environment, the reagents or apparatus.

b) The rinse blank, as the name indicates for rinsing the lines. You should discuss how complex the sample introduction system is in ICPs. >90% sample is wasted and a small fraction goes to the plasma. 

EPA defines it as well. The rinse blank should flush the system between solution changes for blanks, standards, and samples. Allow sufficient rinse time (~ 1 min) to remove traces of the previous sample. Solutions should aspirate for at least 30 seconds prior to the acquisition of data to establish equilibrium

Reference: this detailed report with terminologies

(ICP-MS) with - EPA: https://www3.epa.gov/ttnamti1/files/ambient/pb/EQL-0512-202.pdf