Can a business that does background checks for an emplorier get a copy of my dd214? Are they able to see what my discharge was?

Yes, it is a matter of public record. It can be obtained over the internet for a fee. I can find out everything about you from here at my computer with only your name and address. Just Google any name you like and you will see what I mean. Try your own and it will come up with your address for the last few years, age, phone number and so on. I can find out what if any property you own, if you have any leins or judgements against you. Your criminal history, credit history, and your military record. Welcome to the information age.