ISO and EI are different things and have different meanings. I find that it really helps understand what you are doing if you use the terms correctly and understand exactly what each really means.
ISO is the measured sensitivity of film stock. There is no actual direct equivalent for electronic cameras as the camera manufacturer is free to determine what they believe is an acceptable noise level. So one camera with an ISO of 1000 may be a lot more or less sensitive than another camera rated at 1000 ISO, it all depends on how much noise the manufacturer things is acceptable for that particular camera.
Broadly speaking on an electronic camera ISO is the number you would enter in to a light meter to achieve the a normally exposed image. It is the nearest equivalent to a sensitivity rating, it isn’t an actual sensitivity rating, but it’s what you need to enter into a light meter if you want to set the exposure that way.
EI is the Exposure Index. For film this is the manufacturers recommended best setting for your light meter to get the best results following the standard developing process for the chosen film stock. It is often different from the films true sensitivity rating. For example Kodak 500T is a 500 ISO film stock that has an EI of 350 when shooting under tungsten light. In almost all situations you would use the EI and not the ISO.
On an electronic camera EI normally refers to an exposure rating that you have chosen to give the camera to get the optimum results for the type of scene you are shooting. ISO may give the median/average/typical exposure for the camera but often rating the camera at a different ISO can give better results depending on your preferences for noise or highlight/shadow range etc. If you find exposing a bit brighter helps your images then you are rating the camera slower (treating it as though it’s less sensitive) and you would enter your new lower sensitivity rating into your light meter and this would be the EI.
Keeping EI and ISO as two different things (because they are) helps you to understand what your camera is doing. ISO is the base or manufacturer sensitivity rating and in most (but not all) log or raw cameras you cannot change this.
EI is the equivalent sensitivity number that you may choose to use to offset the exposure away from the manufacturers rating.
If you freely interchange ISO and EI it’s very confusing for people as they don’t know whether you are referring to the base sensitivity rating or a sensitivity rating that is not the base sensitivity but actually some kind of offset.
If you have a camera with an ISO rating of 2000 and you say “I’m shooting at 800 EI” then it’s clear that you are using a 1.3 stop exposure offset. But if you just say “I’m shooting at 800 ISO” it is less clear as to exactly what you are doing. Have you somehow changed the cameras base sensitivity or are you using an offset? While the numbers used by EI and ISO are the same, the meaning of the terms ISO and EI are importantly different.