Question re the (non-)equivalence of Z -> z and Z -> z e (e the empty string)

Background


Consider any linear grammar G of a regular language L in which:


a) the designated "empty" or "null string" symbol e is not an
      element of G's terminal alphabet Vt;


b) G contains the rewrite rule Z -> z, which always terminates a
      derivation in G since z is an element of Vt;


Now consider a grammar G' of a regular language L which is just
like G except that:


a) the terminal alphabet Vt' of G' does contain the null/empty string
      symbol e


b) G' contains the rewrite rule Z -> z e instead of Z -> z.


In any derivation D in G, the deepest subtree in D will be a tree
consisting of one parent with one child:


[ z ]
  Z


In the corresponding derivation D' in G', the deepest subtree will be
a tree consisting of one parent and two children:


[ z e ]
  Z


Question


Can anyone think of any non-trivial reason why the grammars G and G'
should be distinguished one from the other within formal language
theory or automata theory or any application thereof ?


The answer to this question has both formal and empirical
consequences, otherwise I would not be wasting anyone's time to
double-check my own opinion on the matter.


Thanks for whatever time you can afford to spend considering this
matter.

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