Short answer
A Title Register is the written record of a registered title. A Title Plan is the plan showing the general extent of the land in that registered title. They are different documents and are often used together.
What does a Title Register show?
A Title Register can show the title number, property description, tenure, registered owner details, lender or charge information, and certain rights, notices or restrictions.
Official source: https://www.gov.uk/get-information-about-property-and-land/search-the-register
What does a Title Plan show?
A Title Plan shows the general extent of the registered title on a plan. It helps identify the land linked to the title but does not normally define exact legal boundaries.
Official source: https://www.gov.uk/your-property-boundaries
Which one should you order?
If you need ownership or legal title details, start with the Title Register. If you need to understand the general property extent or compare land outlines, order the Title Plan as well.
Common use cases
Buyers, sellers, property owners, neighbours, conveyancers and researchers may use both documents together to understand the registered title record.