Liquid soap
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The closest adjacent product, and it is a genuinely different process rather than a diluted bar.
A different alkali
Liquid soap is made with potassium hydroxide rather than sodium hydroxide.
Potassium soaps are soft and soluble; sodium soaps are hard. That is the whole reason for the substitution.
SAP values differ between the two alkalis, so the lye calculation must be run for potassium rather than adapted, and potassium hydroxide is frequently sold at less than 100% purity, which the calculation has to account for.
What changes in the process
It is normally cooked rather than left to saponify in a mold, producing a paste.
The paste is then diluted with water, which is a step with no equivalent in bar making and which takes time and judgment.
It may need sequestering and it usually needs a preservative, because a diluted product with high water content is a microbial risk that a bar is not.
And no cure, which removes the six-week constraint entirely. That is the single largest operational difference.
The category question is the same
The soap exemption is about composition and representation, not about physical form, so a potassium soap can be exempt soap on the same two conditions.
Which means the same discipline applies: a hand wash sold as moisturizing is a cosmetic.
And a hand wash sold as antibacterial is a drug, which this format attracts more than any bar does.
Note also that many commercial "liquid soaps" are synthetic detergent systems rather than soap, and those fail the composition condition outright.
What it costs you
A new set of containers, pumps and closures, and pumps are expensive.
A preservative decision and the testing behind it.
Shipping a heavy liquid rather than a dense solid, which is worse.
And a viscosity problem, because customers read thin as weak and thickening a potassium soap is real formulation work.