It is a different type of substitution. It's actually a legal concept (like justification).Another great day, JonC.
It would seem that after readying what you wrote. My OP fits nicely within your concept of "representative substitution".
I'm trying to think of a more clear distinction, for me, between the two (Substitutionary vs Representative). What I see at first blush, is a distinction that takes one in a different direction from the typical Limited Atonement debate.
Substitutionary would seem to revolve around payment for individual sin (debating whether it be more like commercial or criminal law). Substitutionary would seem to focus on "particular" sin (like of each individual).
Would you say that Representative, in contrast, might revolve around a concept of "global" sin instead of "particular" sin? That is, representative substitution might forward the idea that Christ's death was "of infinite worth and value, abundantly sufficient to expiate the sins of the whole world." (Dort, 2nd Head, Article 3)? This statement from Dort appears to be global in nature.
Peace to your brother.
Historically Substitution (Satisfaction) was the Catholic view (Aquinas) and Penal Substitution Theory a reform of that view (moving it from merit to divine justice) where Jesus experienced God's wrath as our punishment instead of us not being punished). It is an old position, but also a relatively new position within Christianity. That said, Substitution Theory and Penal Substitution Theory are the most popular views within Western Christianity today (the former being Roman Catholic and the latter the majority of Protestant denominations).