Raw agricultural oils have a limited number of unsaturated chemical bonds between some of the atoms in their carbon chain structure.
These carbons are available for reaction with alkalies such as lye, which saponifiy each pair of target carbons by adding a molecule of water H_O_H. H_ to one carbon, _OH to the adjoining carbon.
The properties of the resulting material, soap, are not very similar to the original oil, it is quite water soluble by comparison, and capable of easily emulsifying regular oil & grease as expected for water rinsability.
If the raw oil is instead reacted with hydrogen gas, one _H goes to each reactive carbon and the molecule after that point is referred to as being saturated with hydrogen. That's why they call it hydrogenated vegetable oil. Things like Crisco which are solid at room temperature and able to cook at high heat because they are hydrogenated, even though the raw oil they are made from is light and does not even solidify under refrigeration.
The lye is not very reactive with vegetable oil that is already saturated (plain mineral oil is saturated naturally).
The heavier fractions or varieties of palm oils can be solids at various room temperatures, and under refigeration the heavier waxes from olive oil often separate from the lighter fractions readily. But both of these waxy fractions are solid naturally just because they have a higher melting point, there has been no hydrogenation and the raw solid oil when melted can be reacted with lye as fully as raw light fractions can.