Fuel is a substance that can ignite in the presence of oxygen. The oxidizer is the source of oxygen. The propellant is a mixture of fuel and oxidizer that burns to propel a body. Hypergolic liquid, non-hypergolic liquid, and solid rocket are the three most prevalent types of rocket propellants.
The hypergolic fuels contain ultra-reactive fuel and oxidizers. In fact, the two only have to come in contact with each other to ignite. On the other hand, the non-hypergolic fuels require an ignition source to spark burning.
The fuel and oxidizer are pumped into a combustion chamber. On burning, the mixture produces hot, rapidly expanding gases that need a way out.
As opposed to the hypergolic propellants, the solid rockets contain a pre-mixed fuel and oxidizer. The pre-mixed substance is moulded into appropriate shapes and thicknesses for the various types of burns. The cut and moulded material is inserted in the rocket fuselage. It may also be bonded to the sides. In the centre of the fuselage, the ignition is provided to ensure that the fuel burns from inside out.
Liquid propellants make it easier to manipulate thrust using the turbopumps. The turbopumps are used to drive the fuel and oxidizer into the combustion chamber. Usually, the only way to control the solid rockets is moulding and shaping. Once they start burning, it is quite difficult to stop them from burning. Some solid rockets use multiple sections of solid fuel and burn them separately to provide better control.
So this is the difference between a fuel and a propellant.