Cost per install
CPI is the media cost divided by the number of attributed installs. It is simple, comparable across campaigns and useful for judging the efficiency of top-of-funnel delivery.
Its limitation is that an install is not a business outcome. Two campaigns with identical CPI can produce entirely different revenue if one acquires users who never open the app again.
Cost per action
CPA measures the cost of a defined action after the install: a registration, a purchase, a subscription, a completed order. It is closer to business value and harder to game.
CPA requires reliable event tracking and enough volume for the data to be meaningful, which is why CPI often remains the working metric early in a campaign while CPA becomes the deciding metric as data accumulates.
Using both
Most mature mobile programmes monitor both. CPI diagnoses media efficiency; CPA judges whether the media was worth buying. Looking at either in isolation leads to predictable mistakes.