There are several differences including the number of variables as well as other nomials, their graphed appearance, and complexity of representation or relationship. A linear equation is the mathematical representation of a relationship that can be visualized, or graphed, as a straight line. A general function is a representation of a relationship between two or more pairs that can result in any type of line when graphed out.
Linear equations have infinite sets of ordered pairs that satisfy their equation. Functions can have smaller sets of viable answers. Functions can include many variables that are independent, while a linear function only has two: the 'x' and the 'y'.
A linear function generally follows the pattern of y=mx+b. Functions tend to be represented in terms of f(x) or whatever variable is chosen. Linear equations tend to be the most basic of functions as they are limited to only two variables; meanwhile, functions can represent more complex relationships as they are not restricted as to the number of variables that can be included.
Functions are commonly used in economics, accounting and the sciences to show these complex relationships. All linear equations, except for vertical lines, are functions, but not all functions are linear.