Mathematics vector calculus and linear algebra difference?

What the two fields have in common is that both fields involve the use of vectors, that is, they use the same foundation in order to describe processes in space.  However, what the two fields do with that foundation is entirely different.

Calculus is generally concerned with the analysis of functions in space.  Vectors are used to describe the direction and rate of change of a function.  The most common and direct application of vector calculus is in physics, in which calculus is used to describe the dynamics of forces and objects in 3-dimensional space.

Linear algebra, on the other hand, is concerned with the structure of spaces in general and with linear transformations.  One application is in computer science, in which linear algebra is used to organize information and to describe and manipulate space and spacial information.  In physics and mathematical modeling, it is used to apply structures to model complex constructs using many simple ones.

I hope that gives you a good idea of what's what.