They’re mostly describing the same underlying controls in different ways.

The flash/ambient balance is set by changing:

• ambient exposure, and/or
• flash exposure.

How you do that depends on the mode:

• Manual camera + manual flash: you change settings directly. Typically shutter speed affects ambient much more than flash, and flash power changes flash brightness. Aperture and ISO affect both.
• Auto/TTL flash and auto exposure modes: you often don’t set flash power directly, so you use FEC to tell the flash to give more/less light, and EC to tell the camera to make the ambient exposure brighter/darker.

So “exposure length and flash intensity” is the general principle; “EC and FEC” is the practical way to do it when the camera/flash are automating those choices.

ISO is not a separate concept—it’s another exposure control. Raising ISO brightens both ambient and flash unless the automation compensates. That can change the mix indirectly, but it’s less isolated than using shutter speed for ambient or flash power/FEC for flash.

Also, some photographers use “flash ratio” to mean the balance between multiple flashes, so the term itself can cause confusion.