If you want to remove an anchor point from a path, selecting the point and applying the Cut command has the same result as using the Delete Anchor Point tool.

Question

Quizplus · Accepted Answer

Using the Cut command (Ctrl+X or Cmd+X) on an anchor point removes the point but also cuts the path at that location, potentially splitting it into separate paths. The Delete Anchor Point tool, however, removes the point while keeping the path intact and connected.

If You Want to Remove an Anchor Point from a Path