I suggest you go back to school and learn what you are talking about. Most of that is total rubbish.
You don't compute Iout/In in an opamp.
Why not? You need to know about impedance matching in some circuits and that is about current capability.
The fact that you do not compute something is not the same as saying you can not compute this, it is just saying that you do not know that it is computable.
You don't call this beefier opamp as having "current gain"
I suggest you look up the term beefier in any electronics text book for a definition.
If you look at a simple/typical opamp datasheet, you won't find this spec listed.
True do you know why? It is not because this parameter does not exist.
They don't call these opamps "current amplifiers" (or having current gain) just because it has a higher output current drive capability.
No they don't use that term but that does not stop it being what is actually happening.
I feel you are taking your rather limited education too literally.