When talking about inflation there are two main types. I usually call them treasury and CPI inflation, but I don’t necessarily know if those are widely used terms. By treasury inflation I refer to the total supply of money, like the inverse of federal interest rates basically. By CPI inflation I mean the change of the consumer price index over time. Both are useful, but depending on the context one may be more useful than the other.
Your first type (treasury) isn’t usually called inflation, AFAIK.
That’s a metric more widely referred to as ‘money supply,’ and it has a number of different types even within that (M0, M1, M2, etc), depending on if you’re talking about simple cash, bank deposits, and other liquid assets. https://en.wikipedia.org/wiki/Money_supply#Measures_of_money_supply