What is the diffrence between equations and expressions?

Equation and expression differs since an equation equates two values: a=b while an expression is a representation of a numerical value like "a"  or "1" without any equated value. An expression does not have equal sign (=).
For a word problem application, when we are translating a "sentence", we set up an "equation". When we are translating part of sentence or phrase, then we are setting up an "expression".
Example:
Four less than a quotient of ten and a number is phrase that can be translated to an expression: (10/x)-4
Given as a sentence: Four less than a quotient of ten and a number is one, we can translate this into (10/x)-4 =1
The "is" indicates the location of the equal sign.
 
Another difference is that we can evaluate a equation with True or False, which is not applicable for an expression. This is the case since we can compare the values of each side of the equation while an expression is just as single mathematical representation.