To correctly reference the Coins variable within my GameManager script from the coin script..That means I have to refer to it directly as GameManager.Coins rather than trying to shortcut by assigning a variable such as gCoins?
exactly. Shortcuts like these only work for referencing nodes, arrays, dictionaries, and some miscellanous types. So :
var a = get_node("something")
var b = a
b.moveandcollide() # will work as shortcut, it will affect the real "something" node
var a = {"apple" : 2, "banana" : 4 }
var b = a
b["pineapple"] = 4 # this works as a shortcut too, it also will affect real dictionary var a
var a = 9
var b = a
b += 10 # this will not work as shortcut, var a will stay 9 and var b will become 19
Editor help often proveides information, whether type is passed as a value or just a reference. Being passed as a reference means it works as a shortcut