So, we need to know the concept of saturated and unsaturated
Unsaturated fatty acids have one or more double/triple bonds and can absorb more hydrogen atoms.
Saturated fatty acids do not have the above-mentioned properties
The difference between soaps made from vegetable oils and from animal fats are that:
Vegetable oil is unsaturated and therefore the soap is liquid
Animal fats are saturated and therefore the soap is more solid