find the "seven" differences

[Han]

In all your examples, I do not see any part where evaluation could be confused with extraction (as you call it). Consider a hypothetical case of someone typing name(a,b)

Evaluation occurs if 'name' is itself a function. Otherwise extraction if 'name' is a list. In the cases where you used name(a=<value>) -- that is an instance of substitution (which is in a sense, an evaluation in which 'a' is replaced by <value>).

Lastly, in CAS view, extraction can be done using name[a,b] so as to avoid any ambiguity between defining a function and assigning a value to, say, a matrix called 'name' at position [a,b]. For example, does name(a,b):=1 create a 2-variable function whose output is always 1? Or does this store 1 into position (a,b) of a matrix called 'name' ?

There is no need for subscript because either the ()'s or the []'s already separate the characters 'a' and 'b' from 'name' (which would be the main reason to have a subscript).