If you don't have a social security number then you need an EIN which is an Employee Identification Number.
If you don't have an EIN then you put your social security number down instead but if you have an EIN number then you put the EIN or employee Identification number down on the tax form.
The people that usually get an EIN are those people that are employed but don't have a social security number so instead they apply for an EIN through the IRS and get a employee identification number which takes the place of a social security number.
So they are similar but not exactly the same if you have the social security number then you don't have to have a EIN.
But if you have no social security number then you need the EIN for tax purposes.