Syndet refers to synthetic detergent. J&J "no more tears" is my classic example. Below is their "improved" formula straight from their website.
No castile will not burn less - Pure castile soap will be less cleansing than say a soap high in coconut or babasu oil.
JOHNSON'S® Baby HEAD-TO-TOE® Wash
Improved formula. Hypoallergenic fragrance. Free of quaternium-15, parabens, and phthalates in addition to being soap-free and dye-free. Dermatologist- and pediatrician-tested. Allergy-tested. This NO MORE TEARS® Formula is as mild to the eyes and skin as pure water. It gently cleanses even sensitive infant skin without drying.
Ingredients: Water, Cocamidopropyl Betaine, PEG-80 Sorbitan Laurate, Sodium Trideceth Sulfate, PEG-150 Distearate, Glycerin, Polyquaternium-10, Tetrasodium EDTA, Citric Acid, Sodium Hydroxide, Sodium Benzoate, Ethylhexylglycerin, Phenoxyethanol, Fragrance