To point out a chemical characteristic (probably more important):
Fats are composed mainly by saturated fatty acids, while oils are composed mainly by unsaturated fatty acids.
To point out a physical characteristic (not that important):
Oils adopt a liquid form at room temperature while fats adopt a solid form ar room temperature.
Notes:
Saturated fats are those with high amounts of fatty acids in proportion. In other words, high proportions of fatty acids for every unit of fat.
Fatty acids are carboxylic acids (with a carboxylic group in it) that contain a hydrocarbon chain.
Hope it helped,
BioTeacher101