The Interleaved Transition System for 2 Independent and Concurrent Transition Systems
By definition, the interleaving operator is not synchronized, so any transition in $TS1\ |||\ TS2$ corresponds to a transition in a single component while the other one remains in whatever state it is.

More generally, in process algebras like CSP, the parallel composition operator $||$ can be parameterized with a set of symbols on which to synchronize - for example, you could consider $TS1\ |[\{a\}]|\ TS2$, which has the same states and $b$-transitions as $TS1\ |||\ TS2$, but only two (synchronized) $a$-transitions $(l_1,q_1)\to(l_3,q_2)$ and $(l_2,q_1)\to(l_1,q_2)$. In particular, $|||$ is the special case $|[\emptyset]|$.

The point is that (together with additional operations like hiding) this allows you to represent a far greater variety of models of interaction.