A shell totally covers something and is quite hard. For example, the outer covering of a nut (peanut, cashew, almond, etc.) is a shell and the nut is completely covered and protected by the shell.
A crust is relatively soft and easy to break through, even though it is harder than what it is protecting. Often, a crust covers the top layer of something (think of the crust that forms on a piece of food as it is grilled or pan fried) but does not cover all sides.
Oddly, in geology, the top layer, which can be many, many kilometers thick, of the Earth (as well as other, rocky, celestial satellites) is called the crust. It is clearly extremely hard and covers all sides of our planet, yet it is much softer than what lies beneath the crust.