There is an asymptotic relationship between synchronous and asynchronous composability. 

This is a visualization of that asymptotic relationship.

But what is the difference between really fast async composability and synchronous composability?  It's that atomicity of messages is enforced at the L2 STF level.

Atomicity in this context means the STF guarantees that some message A is sent/recv iff a future message B is sent/recv.  The STF can do this by expanding the scope of its unit of atomicity (a transaction or a block) to include another chain's unit of atomicity.

In other words, an async atomic message scheme needs to be built on top of the STF.  A sync/atomic message scheme is built inside the STF.