The primary difference between the two is an equals sign. An "equation" has a left side, a right side and an equals sign separating the sides. An "expression," by contrast, doesn't have any "sides" and is simply what the name suggests: An algebraic "expression." Though sometimes it is possible to combine like terms, we are generally not expected to "do" or "solve" anything regarding expressions.
For example:
3x - 7 = 2
This is an EQUATION, because it has a left side, a right side, and an = sign separating the two.
3x - 7
This is an EXPRESSION, because there are no "sides" and no = sign.
