The only important difference in the invoice for small businesses: under no circumstances should sales tax be shown. As this does not comply with the provisions of the VAT Act, a reason must also be clearly stated on the invoice:
A note in the form of “According to § 19 of the UStG no sales tax is charged” is quite sufficient as justification.
Of course, the other accounting rules continue to apply without prejudice to the Small Business Regulation. Strictly speaking, even as a small business owner, you are not “exempt” from sales tax in the strictly legal sense – it's not just collected by the tax office to simplify administration. This is a key difference.
You can also find instructions on how to write a proper invoice and sample wording for small business owners in our article “Create an invoice (instructions)”.