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Let us now see the difference between soap and detergent:
The sodium salt of long-chain fatty acids makes up the soap.Sodium salts of sulphonic acids make up the detergent.
\(-COO^-Na^+\) is the ionic part of the soap.\(-SO_3^-Na^+\) is the ionic part of detergent.
Soap is manufactured from animal fats or vegetable oils.Detergents are obtained from hydrocarbons extracted from crude oil.
In hard water, the effectiveness of soap reduces.Detergents are effective in hard water.
Soap forms a scum in hard water.Detergents do not form scum in hard water.
Soap has a poor foaming capacity.Detergents have a rich foaming capacity.
They are biodegradable.They are mostly non-biodegradable.
Have you ever noticed the term "TFM" mentioned on the soap cover?:
Total Fatty Matter (TFM):
The Bureau of Indian requirements stipulates that the total fatty rely (TFM) on in a bathing bar must be much less than \(60%\), however, not less than \(40%\), while that in a cleaning soap has to be over \(60%\) but less than \(76%\). 
The TFM quantity describes the pleasantness of a soap. It provides moisturizing residences to the product, leaving your skin deeply cleansed but gentle and supple. Higher the TFM, the better the soap is.