Hi LorriJeannine and welcome to my tax board.
The differences in the forms are: you can file a 1040A or 1040ez as long as you are single or married with no dependents and making less than $50k. You can deduct children and child care expenses on the 1040A form. Income must be from wages, interest, dividends etc. and you cannot itemize. Sometimes you meet all the criteria for filing these forms but you may have an expense that pushes you into the 1040 form.
The 1040 form is for filers that itemize. That means that you have more deductable expenses then the standard deduction, which is $7,200 for single and $12,950 for married filers. This form is also for people that have capital gains and income from self employment.