One important difference between solving equations and solving inequalities is that when you multiply or divide by a negative number, then the direction of the inequality must be reversed, i.e. "less than" becomes "greater than", and "less than or equal to" becomes "greater than or equal to".
Actually, from a purist's sense, the reversal rule also applies with equations. Its just that the reversal of "equals" is still "equals". The same goes for "not equal to".
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equations have an = sign, inequalities do not
"What is the difference between inequalities and equations" is a question, not a statement. A question cannot be true or false. It can be pointless, or badly phrased or misguided but that is a different matter.
An inequality with "and" is true if BOTH inequalities are true. Inequality with "or" is true if ONE of the inequalities are true.
The main difference is that when solving inequalities, if you multiply or divide by a negative number you have to be careful, since you then also have to switch the sign (for example, change a "less-than" sign to a "greater-than" sign). If you multiply or divide by an expression that contains a variable, you have to consider the two cases: that such an expression might be positive, or that it might be negative.
radical equations have sq roots, cube roots etc. Quadratic equations have x2.