The distinction matters financially. The drain within your boundary serving only your property is yours to maintain. The moment it crosses the boundary it becomes a lateral drain and the water company's problem.
If a blockage is in the lateral, the water company clears it at no cost. Many homeowners pay private contractors for work the water company would have done free simply because nobody explained the boundary rule.
Where the boundary is unclear, a CCTV survey with sonde location will establish exactly where the defect sits relative to it.