What is the difference between the Tax Rate "Exempt", "Zero Rated", and "No Tax" in Sage Accounting

They mean different things.

• Exempt is recommended for things that are exempt from tax. Use it for Items that are non-taxable.

EXAMPLE: Bank fees are exempt from tax. 

• Zero-rated is recommended for something that is taxable at 0%.

EXAMPLE: Milk from the grocery store.

• No Tax is for things completely outside the tax system (like adjustment lines on an invoice).
  Keep in mind, No Tax sales transactions are not included in the Total Sales box (101) on the tax return.

You can create a transaction and choose a different Tax Rate at each line item of a same invoice.

TIP: By selecting No Tax on your transactions, your sales on the tax return will not match your sales on the Profit & Loss (Income Statement) report.
If you want them to match, you should choose either Exempt or Zero-rated on your transactions.