[R] terminology for frames and environments

[Gabor Grothendieck]

In ?exists it says:

inherits: should the enclosing frames of the environment be searched?

I believe what it is saying is that if inherits is TRUE and it fails
to find the variable it will look in the parent environment and
the parent of the parent, etc. (as opposed to looking in the calling
frame next and the caller of the caller, etc.)

Now I thought that standard terminology in R was:

1. enclosing environment or parent environment if one wanted to
refer to the parent relative to the parent/child hierarchy 
of environments

or

2. calling frame or parent frame if one
wanted to refer to a parent relative to the environments
corresponding to the functions in the stack 
of currently outstanding function calls

but here we seem to be referring to a parent frame as a #1. 

Could someone please clarify what standard terminology is?

Thanks.