The last plane of motion to consider is the transverse plane. These exercises move you in rotational directions. Yes, pectoral fly movements count as transverse plane, but I would not consider them "core". The best way to think of these exercises is rotating the upper body on the lower body, or vice versa.
To put these into perspective as a functional exercise, think of starting your lawnmower, or swinging a baseball bat. The motion can be with one or both hands. Functionally we use these muscle as both stabilizers and prime movers. Here is an example of a stabilizing exercise: it's called the Pallof Press or anti-rotation
As you can see there is no rotation going on, yet the increase in distance of the handle from the chest to arms straight creates a longer lever arm in the correct axis. This makes you fight against rotating the torso, aka "anti-rotation".
Other good examples include actual rotation while standing or laying, with cables,weights or
bodyweight.
Lastly, when figuring out your core routine, please consider this general rule: more integration, less isolation. You will notice that all of these exercises for the core are moving the upper body on the lower, or vice versa. If you use this principle for all exercises, all of them will become more functional, and "core". Just remember to watch your posture when doing any of these. If you can't have good posture when you are exercising, there is little chance you will have it the rest of the day.
