Lipids are groups of naturally occurring organic molecules that mainly function for storage of energy and cell signalling and are the building blocks of bio layers such as cell membranes. It is a wide groups of compounds which includes waxes, sterols, fats, monoglycerides, fat-soluble vitamins (A, D, E and K), phospholipids and many more.
Fat are one of classification (sub group) of lipids which are triglycerides, triesters of glycerol and of fatty acids.
Now we can say that all Fats are Lipids because it is a sub group of lipid. We cannot say that all lipids are fats because there are other subgroups of lipids which are not fats. It is like saying: "All elephants are mammals but not all mammals are elephants."