Short answer is size.
Of the ones you list the J is the smallest followed by L & K.
The J frame is typified in the snub nose revolver. L is a Medium size frame used in 38 specials & small 357’s & the K is a medium large frame.
Advantages are concealability. Smaller is always easier to conceal. Larger is heavier to carry but easier to control rapid fire.
Its always a trade off…