Combinator terminology: What is "strong" about strong composition?
I'm not familiar with the &quot;strong&quot; terminology. However, the 'obvious' answer to the other question is that it both duplicates the $x$ argument and exchanges the relative positions of (one copy of) the $x$ and $g$ arguments:
$$\mathsf s\ f \ g\ x = f\ x\ (g\ x)$$
The other combinator it's usually paired with:
$$\mathsf k\ x\ y = x$$
discards an argument. Together, this is all three of the structural rules for a variable context (contraction, exchange, weakening), and it includes composition as well.