Stamp duty is the name given to the tax you pay when you buy property or shares. When you buy a property you pay Stamp Duty Land Tax. If you buy shares you usually pay Stamp Duty (if it's a paper transaction) or Stamp Duty Reserve Tax (if it's an electronic, paperless transaction).
You pay stamp duty land tax when you buy a property such as a house, flat, other building or land. If the purchase price is less than a certain amount, you don't pay any stamp duty land tax at all, otherwise you have to pay a percentage of the purchase price.
However, if you're buying a property in an area designated by the government as 'disadvantaged' or one that is ‘zero-carbon' you may qualify for relief so that you won't have to pay as much stamp duty land tax.
You pay stamp duty or stamp duty reserve tax when you buy shares. You pay stamp duty when the shares are transferred to you using a stock transfer form, while you pay stamp duty reserve tax when the shares are transferred to you electronically without using a stock transfer form.