Is there a difference?
This is a very technical question. Since I am not an RF engineer, I reached out to a few people for the answer. Before I provide an answer, let me explain what the terms mean, for those who don't know.
Effective radiated power (ERP) is a measurement of the output of RFID reader antennas, and is equal to the power supplied to an antenna multiplied by the gain of that antenna (gain is a measure of intensity), compared to a standard antenna. Effective isotropic radiated power (EIRP) is the output of an antenna compared to that of a theoretical antenna that radiates equally in all directions.
Neeraj Sood, a research at McMaster University's RFID Applications Lab, reports that the calculation of ERP and EIRP are independent of antenna polarization—which he says is related to the electric field produced by the antennas, whereas ERP and EIRP are related to power output. "As long as the power transmitted by any antenna in the direction of its maximum gain is known, we can find its EIRP," he states, "and EIRP helps us in comparing different types of antennas—regardless of whether they are circular- or linear-polarized—by using the same baseline (i.e., an equivalent isotropic antenna)."
One thing to consider: If you are trying to calculate ERP or EIRP to ensure conformity with government regulations for radio devices, be sure to check the law to determine whether it distinguishes between linear-polarized or circular-polarized. If the law is based on linear polarization, it might be possible to increase the antenna's power output or gain when using a circular-polarized antenna. But be sure you understand the regulations fully, because it would be easy to boost the output and then find out that your calculations were off, and that you were operating an illegal device.
—Mark Roberti, Founder and Editor, RFID Journal