I'm late to the party. Is it incorrect to refer to "Box 2 of the Am pentatonic scale" as "Position 2 of the Am pentatonic scale"? I am aware of a classical guitarist would say position 1 if the root of the scale starts on the 5th fret. Let me know as I may be inadvertently causing confusion.
The problem you are running in to is that there are very many different approaches to teaching the guitar, each with their own and often conflicting terminology. Even in classical guitar approaches there will be different definitions of what "position one" is.
The term "position" on the guitar is used in many ways. In some case the position refers to what fret the chord or scale is starting from, so position 5 would be 5th fret. In other cases the positions are specific to the method being taught, and can be oriented around different chord shapes, scale shapes or arpeggio locations. I'd recommend not trying to make a direct correlation, and only refer to the "boxes" as boxes when discussing the method you are working with.
Ultimately all of the various guitar systems are designed to let the student develop the knowledge of where the notes are on the guitar and how they fit into scale and chord patterns of western music. Don't get too locked down to the terminology you are starting with, as different players that you work with will have learned different systems, but we all seem to manage to figure it out once the music starts.
In the CAGED system the A shape is referred to as position 4. The use of the term "boxes" is new to me, and may be specific to the book or web page you are working out of.
Some of the instructions I looked at show the A form for C major/A minor starting in the second zone/box up, which may be called second position in that instance.
You may be working with a Blues guitar method that uses the term "boxes", in which case stick with the terms the method uses to avoid confusion.