A regular integral is just the total area under a fixed curve in space...
A line integral is the total area under a FIELD carved out by a particular curve.
A line integral can be performed anywhere in space, while a regular integral is restricted to 2 dimensions.
This is just a small qualitative difference... If you would like to see the real differences, you could try them out in frequent examples to see what each one is trying to add up and where the curves are allowed to be.