Not sure about the S3 being the chordae tensing, but that seems plausible since all the blood rushes into a dilated ventricle causing some sort of "rebound" contraction.
Anyways the S3 as I learned it is an early diastolic sound of blood rushing into a dilated ventricle with increased compliance or with increased volume of blood(due to something like mitra regurg. or tricuspid regurg). The blood passively spills into this chamber with lots of fluid/volume.
S4 is late diastole, and thats when the atria contracts. It can either be due to a rebound (e.g. in a concentrically hypertrophic heart) against the muscle of the heart or due to fluid overload, because atria contracting against excess fluid could also cause a turbulent sound.
Therefore, in a concentrically hypertrophic heart you would definitely hear an S4, but probably not an S3 since there really isn't fluid overload in the ventricle.
In mitral regurg, you would hear an S3, and maybe an S4 if it is an early mitral regurg.
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Another way to put it, kind of simplifies it in my mind:
I imagine S3 to be like a waterfall...all that fluid hitting more fluid passively.
I imagine S4 to be like hitting a drum. The atria pushes that blood into the wall of the ventricle hitting either muscle or more blood causing a sound.