An unsaturated carboxylic acids contains only the #1^@# of unsaturation. For instances, #"acetic acid"#, #"H"_3"CC(=O)OH"#, has formula #C_2H_4O_2#, i.e. #1^@# of unsaturation.
Both #"palmitic"#, and #"butyric acids"# are saturated by this definition. #"Palmitic acid"#, i.e. palm oil, is the typical saturated fatty acid, and this is the food component that nutritionists encourage us to avoid.
On the other hand #"oleic acid"#, #C_18H_34O_2#, is the typical UNSATURATED acid (and cis with respect to the necessary double bond), that is found in olive oil, and which nutritionists promote.